You say that you feel this is a burden, that he handed you a pile of steaming sh*t. So refuse to carry it.
Not to be rude - I'm sure you are a very attractive woman - but I've heard drunks make passes at people they would run from while sober. I tend to agree with any key that while for you this is huge and life changing, for him it may only have been booze talking.
I think I'd go over with my husband and say in a joking tone - "you'd better cut down on your drinking, bud - you were so plastered last night that you made a pass at me." Make him the butt of a joke, that way you hand the steaming pile of sh*t right back to him.