Sunny, Wish I was closer to SoCal, I would advise you to invite H, but me too, as your date!
That not being the case, I can just say that I just had a (very) small belated b'day part here in FL (the real one was in TX). I told W about it and when she asked if she was invited, I just said "I'd prefer if you didn't come." I think that was a real stab to the heart for her since it was with neighbors and our kids at a neighbors house.
My guess is that this would be a similar result for you too. Probably he will sulk around for a week or so if you don't invite him, but it is necessary for him to understand that while you will remain friendly, you will not be friends as long as he is carrying on with OW!
Love ya, SD
Me 41 W 41 Kids: S9 S7 Married 16 years Bomb dropped 2/2/07 Still living together! current thread