@Jack1034,
Then I think you've got to lay your cards on the table. And that's risky and it might not work out the way you want it to. But right now, you're in limbo. And that's rather unfair to you.
At the very least, when he claims to not remember this or that, if I were you (and I'm a het woman, so take this FWIW), I would at minimum express concern. Drinking to blacking out and not remembering is rather dangerous.
Of course you know, I know, the lamppost knows, and the American people know, that he's just clumsily trying to cover up what happened. And the out it gives him is not so wonderful. If he admits to drinking to excess then your concerns are justified and then if you suggest he get treatment, he'll balk. If he doesn't admit to drinking to excess, then he's left with two options: either he admits he got into bed with you or he claims some other memory problem.
Somehow, the truth will out (no pun intended).
Do you like in an area (or have a group of friends) where coming out would be dangerous or hurt his career/family/etc? If so, then I would respect that. But if you're in a major western city (New York, Toronto, Paris, etc) then coming out is still a big deal, but it's not career-ending or life-threatening like it would be in Basra.