It is obvious that the common Hobbits (and men) knew nothing of the true nature of the Istari. When the Istari arrived in Middle-earth they were considered "strange elves" (as a matter of fact, Gandalf means "staff elf") or "strange men", wise, long-lived and mysterious, but the treatment that Barliman Butterbur or Denethor gave to Gandalf would have been very different from that which he actually received had it been known that he was a Maia.

But it is clear from the book that Frodo knew the true nature of Gandalf and Saruman. When the Scourging of the Shire, he refers to Saruman as:

someone of a race against which we would never have dared to raise our hand.

Is there any passage from Tolkien's books, or other writings, that allows us to know when this was revealed to Frodo (or Bilbo)?

It is unclear whether anyone even knew Gandalf was a Maia

...save Elrond, Círdan, and Galadriel themselves. Tolkien says this in the Unfinished Tales:

Wizard is a translation of Quenya Istar: one of the members of an "order" (as they call it), claiming to possess, and exhibiting, eminent knowledge of the history and nature the World. The translation (through suitable in its relation to "wise" and other ancient words of knowing, similar to that of istar in Quenya) is not perhaps happy, since Heren Istarion or "Order of Wizards" was quite distinct from "wizards" and "magicians" of later legend; they belonged solely to the Third Age and then departed, and none save maybe Elrond, Círdan and Galadriel discovered of what kind they were or whence they came.

_{Unfinished Tales, Part II, The Istari}

Which would make sense. The Istari came in secret to Middle-earth, and no one (save the aforementioned trio) found out about that. And you may wonder how these three found out, when the Istari didn't tell anyone about their past.

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  Cirdan

  
  
  

  The easiest to explain. He's the guy who's in charge of the Grey Havens, and is one of the wisest (and oldest) of the Elves remaining in Middle-earth. It's clear Cirdan saw what Gandalf was, as he gives him Narya, one of the 3 Elven Rings - themselves being 3 out of the 20 Rings of Power - when Gandalf first arrives in Middle-earth (which is in itself a tell-tale sign of where he came from).

  
  
  

  
  

  "Take this ring, Master, for your labours will be heavy; but it will support you in the weariness that you have taken upon yourself. For this is the Ring of Fire, and with it you may rekindle hearts in a world that grows chill. But as for me, my heart is with the Sea, and I will dwell by the grey shores until the last ship sails. I will await you."
  ― Círdan, Appendix B

  
  

  
  


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  Elrond

  
  
  

  Another one of the wisest Elves in Middle-earth, it's likely he knew of what Gandalf (and the Istari were) from perception. He's the son of Earendil, the only Man ever admitted into Valinor (and lives to tell the tale), and he's been around for 3 Ages. He's also the bearer of Vilya, one of the 3 Elven Rings, and this connection may have given him insight of what Gandalf was.

  
  


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  Galadriel

  
  
  

  Similar to Elrond, and Cirdan, Galadriel has lived in Middle-earth for 3 Ages, and she's far older than Elrond. The bearer of Nenya, and also wise enough to discern the nature of Gandalf and the other Istari.

  
  

Addressing your quote:

[...] someone of a race against which we would never have dared to raise our hand.

The Istari were known as Wizards to everyone in Middle-earth. I do not believe Frodo knew exactly that Gandalf was a Maia, just that he was of a nobler race than the Elves, Men and Dwarves (and Hobbits). Gandalf He exudes wisdom and power, as Pippin himself remarks:

Yet by a sense other than sight Pip­pin per­ceived that Gan­dalf had the greater power and the deeper wis­dom, and a majesty that was veiled. And he was older, far older. ‘How much older?’ he won­dered, and then he thought how odd it was that he had never thought about it be­fore. Tree­beard had said some­thing about wiz­ards, but even then he had not thought of Gan­dalf as one of them. What was Gan­dalf? In what far time and place did he come into the world, and when would he leave it?

_{The Lord of the Rings: The Return of the King, Book V, Chapter I}

From that quote we can see it's quite obvious Pippin himself isn't sure of what Gandalf is. He isn't an Elf, Men, Dwarf, or any other race present in Middle-earth. What then is he? He's never told, and only knows Gandalf as "one of the 5 Wizards that were sent to Middle-earth".

Frodo likely thinks the same. Learned as he is in the lore of Middle-earth, I do not believe he knew more of what a "Wizard" was anymore than Treebeard, himself a very old being.

‘Saru­man is a Wiz­ard,’ an­swered Tree­beard. ‘More than that I can­not say. I do not know the his­tory of Wiz­ards. They ap­peared first after the Great Ships came over the Sea; but if they came with the Ships I never can tell.

Notes on Gandalf

It's also said that Men mistook Gandalf and the other Istari to be of the Elven-kind. Which is itself incorrect, of course, but further reinforces my stand that no one really knew what the Istari were. Certainly not Barliman, and not even Denethor.

Mostly he journeyed unwearingly on foot, leaning on a staff; and so he was called among Men of the North Gandalf, “the Elf of the Wand”. For they deemed him (though in error, as has been said) to be of Elven-kind, since he would at times works wonders among them, loving especially the beauty of fire; and yet such marvels he wrought mostly for mirth and delight, and desired not that any should hold him in awe or take his counsels out of fear.

_{Unfinished Tales, Part II, The Istari}

So, to answer your question, Bilbo and Frodo did not know that Gandalf was a Maia (by Word of God), and never found out, as far as the narrative tells us¹.

I will leave you with this quote, courtesy of Gildor.

"Do not meddle in the affairs of wizards, for they are subtle and quick to anger."

Notes:

¹ We aren't told whether Frodo, Bilbo or Sam ever found out, in Valinor, of Gandalf's race, but logically, we could assume they did. After all Gandalf would have used the name of Olorin by his fellow Maia, and would at least told his friends more about himself by then. (Hat-tip to Buzz in the comments)

SHORT ANSWER:

I don't know if Bilbo and Frodo ever learned that Gandalf was a Maia.

LONG ANSWER:

In The Return of the King. Book Six, Chapter 8, "The Scouring of the Shire", Frodo says of Saruman:

...He was great once, of a noble kind we should not dare to raise our hands against. He is fallen, and his cure is beyond us; but I would still spare him, in the hope that he may find it.

The Fellowship of the Ring, Prologue, Note on the Shire Records, describes the original Red Book of Westmarch.

It was in origin Bilbo's private diary, which he took with him to Rivendell. Frodo brought it back to the Shire, together with many loose leaves of notes, and in S.R. 1420-1 he nearly filled its pages with his account of the War. But annexed to it and preserved along with it, probably in a single red case, were the three large volumes, bound in red leather, that Bilbo gave to him as a parting gift. To these four volumes there was added in Westmarch a fifth containing commentaries, genealogies, and various other matters concerning the hobbit members of the Fellowship...

...But the chief importance of Findegil's copy is that it alone contains the whole of Bilbo's 'Translations from the Elvish'. These three volumes were found to be a work of great skill and learning in which, between 1403 and 1413, he had used all the sources available to him in Rivendell, both living and written. But since they were little used by Frodo, being almost entirely concerned with the Elder Days, no more is said of them here.

So Bilbo wrote the original version of the The Hobbit, Frodo wrote the original version of The Lord of the Rings, and Bilbo translated into the Common Tongue and/or edited and/or wrote the original versions of most writings about the Elder Days such as the Quenta Silmarillion.

Frodo would have been the original author of The Two Towers, Book Four, Chapter V, "The Window on the West" with this dialog:

'The Grey Pilgrim?' Said Frodo 'Had he a name?'

'Mithrandir we called him in elf-Fashion,' said Faramir, 'and he was content, 'Many are my names in many countries, he said. Mithrandir among the Elves, Tharkun to the dwarves; Olorin I was in my youth in the West that is forgotten, in the South Incunus, in the North Gandalf; to the East I go not.

Later Frodo returned to Rivendell and spent some time with Bilbo, and Bilbo gave Frodo his 'Translations from the Elvish'. If the Valaquenta that named Olorin as a Maia was among Bilbo's translations, and if Frodo read the Valaquenta during his first or second stay in Rivendell, and if Frodo's memory was as good as mine, he might have suddenly thought: "What! Gandalf's original name in the West is the same as the name of a Maia in the Undying Lands in the West! Does that mean that Galdalf and other wizards are Maia?"

And if Frodo ever asked Bilbo if Bilbo had heard of all Gandalf's names and mentioned Olorin, and if Bilbo's memory was as good as mine, Bilbo might have remembered a Maia named Olorin in the Valaquenta or other sources, and Bilbo might have told Frodo that Gandalf's original name was the same as that of a Maia. And they might have wondered about that.

But there is no proof that either of those events happened.

If any accounts of the wizards that actually say they were Maia from Aman were among the contents of the Red Book of Westmarch, they would have been written or translated by Hobbits so eventually some Hobbit or Hobbits believed the Wizards were Maia. But on the other hand it is possible that Tolkien found those accounts not in the Red Book, his main source, but in other sources available to him, and that no Hobbit ever believed or knew that Wizards were Maia.

Remember that The Fellowship of the Ring, Prologue, Note on the Shire Records, says:

This account of the end of the Third Age is drawn mainly from the Red Book of Westmarch.

This shows that Tolkien used other written and/or oral sources for The Lord of the Rings and maybe other writings, some of which might not have come through Hobbits, let alone through Bilbo or Frodo.

Bilbo gave his 'Translations from the Elvish' to Frodo when Frodo left Rivendell to return to the Shire. And Frodo would have had very little opportunity to read them on the trip before the confrontation with Saruman at Bag End. He was mostly riding all day and sleeping around a campfire all night. If Frodo read a book while riding, or for an hour or two each night around the campfire, that would have been unusual enough to be remembered and written down in The Lord of the Rings, I think.

It is quite possible that Frodo realized that Saruman, and thus Gandalf and the other wizards, were Maia almost immediately after saying that the Wizards were a very high order of beings.

SPOILER ALERT!!

Frodo had heard from those present at the battle outside the Black Gate what happened when the Ring was destroyed and Sauron defeated:

In The Return of the King. Book Six, Chapter 4, "The Field of Cormallen":

...And as the Captains gazed south to the Land of Mordor, it seemed to them that, black against the pall of cloud, there rose a huge shape of shadow, impenetrable, lightening-crowned, filling all the sky. Enormous it reared above the world, and stretched out toward them a vast threatening hand, terrible but impotent: for even as it leaned over them, a great wind took it, and it was all blown away, and passed; and then a hush fell.

Frodo was certainly told about that, and Frodo certainly learned that Sauron was a Maia.

As I remember, when sneaking into Mordor, Frodo and Sam talked about the story of Beren and Luthien, and noted that the light in the phial that Galadrial gave Frodo came from the Silmaril in the story of Beren and luthien. And Sauron was a character in that story. So it is possible that even Sam had heard Sauron described as a Maia, and had been told what a Maia was.

A few months after the overthrow of Sauron, Wormtongue killed Saruman, and then:

To the dismay of those that stood by, about the body of Saruman a grey mist gathered, and rising slowly to a great height like smoke from a fire, as a pale shrouded figure it loomed over the hill. For a moment it wavered, looking to the West; but out of the West came a cold wind, and it bent away, and with a sigh dissolved into nothing.

So sometime after first reading The Lord of the Rings, and before I ever read about Valar and Maia, I deduced that the Wizards were lesser members of the same class of highly powerful supernatural beings as Sauron - whatever type of supernatural beings that was.

Frodo could have done the same, and Frodo knew that Sauron was a Maia, so after Saruman's death a minute or so after Frodo said that Saruman was a member of a high order of beings, Frodo had the necessary knowledge to deduce that Saruman and Gandalf were Maia.

But of course having the necessary information doesn't guarantee making the deduction, and Frodo did not get one part of the necessary information until after he made the statement about Saruman being of a high order.

So considering everything, I don't know if any of the Hobbits ever learned that the Istari or Wizards were Maia, and I don't know if Frodo knew that the Wizards were Maia when he said:

...He was great once, of a noble kind we should not dare to raise our hands against. He is fallen, and his cure is beyond us; but I would still spare him, in the hope that he may find it.

Note: While writing this I once wrote "Biblo" instead of Bilbo, which seems rather appropriate.

See also here:

https://english.stackexchange.com/questions/295737/ol%C3%B3rin-i-was-in-my-youth-in-the-west-that-is-forgotten-what-is-forgotten1

And here:

Who in Middle-earth knows the Istari's origin?2