Quote: Why does H feel that I don’t accept ‘who he is.’
Because you don't:
Quote: avoiding and stuffing his feelings, and then letting it leak out when others were around – was not acceptable
Perhaps it's not reasonable to accept someone the way they are all the time.
Is it easy for him to talk to you? Does he feel understood when he does? There are techniques to make someone feel understood - usually by restating in your own words, without judgement, what he means and then asking him if you got it right. That may be why he felt he needed alcohol to say those things.
Then again, sometimes guys step out of line. My guess is the sooner it's corrected the better. So what you MIGHT have done when he started making his cracks is said something like, "Two can play at that game, honey. Let's stop now." And, yes. It is a game.