The highest I can think of that I have jumped in a lesson was an oxer which was 3'4.
Another time four of us were on a course and we had a triple-bar which was 3'0. I was on a POA who stood all of 14.0 hh! (And I am 5'9 so you can imagine how interesting that jump was lol) that was years ago though. I no longer take lessons.