From my life experience, without looking at any statistical data, I have the impression that it is extremely rare within heterosexual couples for the woman to be taller than the man (in the cultures that I'm most familiar with, which are the UK and the US).
When I've pointed this out, people have generally said that this isn't surprising because, of course, most men are taller than most women. However, I would disagree because a height of, for example, 1.7m is only slightly tall for a woman and slightly short for a man. Therefore, if people weren't selecting height-wise, I don't think it would be particularly rare for the woman to be taller.
I wonder a) What is the empirical probability (taking either the US or the UK or even the entire world, or a specific population that a poster knows about) that in a randomly chosen heterosexual couple, the woman is taller?
b) What is the probability under the assumption that the height of the man is independent of the height of the woman?