i think he definitely owes you a big one, and it's his own fault if you're shaky about the relationship. on the bright side, he seems to recognize that!
i think that since you've held on with him for so long, and he has voiced strong desire and intention to make it up to you, that the relationship is probably worth another shot. that is, if you personally think it is. and everyone is human, after all... if his heart was not really in what he did - if it was a stupid trashed mistake - then it doesn't have to mean something permanent about his personality, you know? we all royally screw up from time to time. and i think it's your prerogative to be able to exist in the relationship without nagging fear of him cheating again... which i think could be helped by having a sort of contingency plan. just like saying to yourself, okay, one more chance, but if you do it again, you're gone, and that's that. so you're in charge.
i also say this based on an accident i had with an NFJ friend of mine. it takes her a very long time to deeply trust anyone and she "let me in", so to speak, on things that she would never tell others, because she totally trusted me never to tell. except one day, in the excitement of talking with an old friend, i got stupid and let something bad slip. it got back to her in less than a day. it was never, ever my intention of hurting her or breaking her trust, and i still wish i could go back and stop it before it happened, because i know how much it did hurt her. and now a year later, i think she trusts me almost as much as back then again, but i'm a hell of a lot more careful about what i say to others when it's involving "confidential" info. i think the same could go for your boyfriend. hopefully you can get back to trusting him again (if you want to), and hopefully he is already much more aware of himself when he drinks.
that said, personally, any hint of something like this happening again and he would be out my door so fast he wouldn't even realize what was hitting his ass on the way out. :drop-kick: