I’m the same as CalBal and I’m from NY state (but not city).
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Midwesterner view: your phrasing is normal. I’ve met people who have a lot of trouble with parsing it, but you’re using it the way I’m accustomed to.
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Quarter to/til/past are my native dialect (another NY-state-but-not-city human) but “quarter of” is definitely a Thing. I don’t know if it’s regional or not.
My professional opinion is that prepositions are tiny terrifying beasts. (If I were still in academia, yes, I would consider actually putting that exact wording in a presentation.) Of the four most basic word classes (nouns, verbs, adjectives, prepositions), they’re the ones that are in many ways most elusive: they have relatively little non-grammatical content and the rules that govern them are often capricious. It’s not that there aren’t any rules, because there absolutely are, and there are broad generalizations and statistical tendencies all over the place, but the particular choice of preposition in a lot of contexts is just stipulated by the dialect (please see: different from/than/to). In English, “of” is the default preposition used to connect nominals, so it’s completely unsurprising to me to see it in this context (even if I have a more particular set that I would use).
For those who wanna be nerds, prepositions are fucking wild because they indicate spatiotemporal locations and vectors. I love this because it’s as if language figured out spacetime before we did. 
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I see it as an education issue. When he was in elementary and learned to tell time, this way of telling time should have been taught to him. He should know it, but maybe his school or teacher that year skipped it. It is a hard concept for second graders, trust me on that, and I could see the appeal of just skipping over it. Elapsed time is fun to teach, too. 
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Wait, is it that Clare’s DH just doesn’t know the “quarter” system entirely?
Here I was assuming it was a preposition thing.
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This is definitely true. My coworker and I just agreed that it’s “quarter of” and “quarter after.” Why is “after” the opposite of “of”? No idea!
Thank you for your fascinating linguistic input! 
“Quarter of,” specifically, should have been taught to him? “Quarter to” or “quarter till” make sense to him–they’re just not what I say. It is definitely a preposition thing.
Regardless, he’s a military brat and moved around a lot until he was about 10, so it’s entirely likely for a concept like that to have been skipped.
raises hand
I’m a Midwesterner and I don’t know “quarter of”
Only quarter to and quarter past.
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Oregonian here. I’ve only heard a quarter to or quarter till and quarter after. I’ve never heard “quarter of”
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I do quarter-to and quarter-after, as a Texan-turned-Upstate-New-Yorker-turned-Coloradan.
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Same as Oro, we are in same state.
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Me, three!
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!!!
Do you know if this is true for all languages (about prepositions) or pertaining mainly to English? Or all Indo-European languages? Or only some of them? It seems to hold true for Italian - for example, there are the common, most likely definitions for many prepositions (a = to, di/da = from/of, per = for). But then you have things like, when speaking about foods, if a food has a major component that it is described, it uses “a” (eg. la torta al cioccolato = chocolate cake). Similarly, “vado dal meccanico”, which is how one would say “I go to the mechanic”, but in this case da is more like “by”.
(Hm. Now that I think on it more, Italian prepositions are a hot mess and seem less regular than English). Di, da, a, and per all have sometimes equal definitions used in specific contexts. They do have more frequent ones, but like, you basically have to memorize all contexts. It is kind of a nightmare. Easy to understand in context, but difficult to pull out for recall.)
/derailment
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I think it’s not so much the opposite, but just how you’re seeing it? Like, “quarter to” makes sense that is goes along with “quarter after” because you’re talking about time as a picture of a circle, so therefore the fractions of that circle. One more quarter to get to the next hour, one quarter after the hour. But you can say that “quarter of” is the same as “quarter to” because when you complete that quarter of the circle, you will be at that hour you’re talking about. Does that make sense? Would it make sense to your husband?
Well, I don’t know. It was a reading comprehension error on my part. I thought you were saying he didn’t know that way of telling time at all. I don’t think my kids do, for example, although I could at their ages. But I do know both your way and his way, and I taught all of those ways. Sounds like it’s a bit regional. For what it’s worth, I grew up in Arizona.
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So you are all saying that prepositions are hell even for native English speakers?
Now I can feel less guilty when I struggle with them 
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I say quarter to (not of) or quarter after (not past), but probably equally as often I just say 2:45 or 2:15. And I think I never say half past? Always just 2:30. I am in Michigan.
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Yes. My husband says “on line” when he’s talking about waiting in a line. He’s from the Northeast of our country, and I’m from the Southwest. I would never say “on” line when I mean “in” line; I find it wrong wrong wrong. But I don’t think it’s actually wrong, it’s just a matter of where we grew up.
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To/til/after. Canadian with English and West Indian roots.
May have read of in an American book
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Yes. Prepositions in another language are, generally, hellish for non-native speakers of that language.
It’s a general thing about language – spatiotemporal meanings are very core to that class of words.
I can’t really say much about Italian prepositions and their fine meanings, because I don’t speak Italian, and even to a very competent non-native speaker the full range of meanings for a preposition – especially a very common one – is really hard to understand.
One big problem is that a lot of prepositions get bleached into being grammatical case markers (you know, that crap we say we don’t have in English). This is actually likely pretty true for “of” in English, and my guess is that it may be true for “a” in Italian from what you wrote above. In English, we often just shove “of” between two nominals when they’re supposed to have some vague relationship to each other – often but not always possessive.
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Standard Philadelphia usage.
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You know, I can’t recall if anyone back home actually said that it if I just ran into it in the 3 other time zones I’ve wandered through.
My parents were gloriously Southern in their time-telling. Just round to the nearest half hour.
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