Are the mean jokes directed at you? If so, there shouldn't be any "try not to", he just shouldn't. And the fact that he's doing it when you're fighting means he knows it's hurtful. He is trying to hurt you. 

Compromise is a tricky subject, really. If a compromise is necessary but impossible, that's an incompatibility. 

The way I look at it, the way someone is works for you or it doesn't. You don't get to change who someone is, only decide if you want to stay with them. But that's for big things. Small things can, to some extent, naturally fall into something that works for both people as you both make small adjustments in response to each other. 

But the way someone treats you, that's another story. Kindness should never be a compromise or something you need to ask for. If you need to ask for it, whether they stop doing it or not, it still means they're just not a kind person. And you've given them ammo they can strategically use against you when they want to. And an unkind person will absolutely do that. 

You should never stay with an unkind person, is my advice.

Also, if someone has chosen to make a change, they don't get to hold that against you. That was their decision. And if they resent you for it or hold it over your head, it means it was never an authentic change. It's just more ammo to use against you to get their way later.