Well, lots of people split the claiming of the kids - it's commonly done - and if you let him claim one, it might make for a larger total return between the two of you. So what if you calculate how much you lose by claiming only one child instead of two, and then offer to let him claim one in return for him paying you the difference?
For instance - if you get an additional $1000 back for two kids instead of one - let him claim that one, he gets, say, $3k back because he can claim HOH also, then he pays you $1000 of that. You don't lose anything and he gains something. Win win.
