Hi, I may not have the words of wisdom that others seem to have here, but I'm responding because my H also has a drinking problem. In fact, he's looking at a DWI because of it. He has screwed up royally. So I have to live with his A and other woman, and whatever legal consequences come of the DWI.
How can you cope? I am trying to follow the advice of everyone here. DBing, GAL, act as if, etc. That seems to be our only course of action. But it hardly seems enough, does it? Don't you just want to give him a kick in the head (or elsewhere) to get him to wake up?!
It sounds like he is being very selfish. That seems to be the norm for people in an A. Don't count on him to make you feel better. He is only thinking about himself. You can work on you without him.
It's hard to get the energy to take care of ourselves with all the crap in our lives. But again, what choice do we have? I know by doing one little thing for myself, it makes me feel better. Don't look at the bigger picture, take one step at a time. Do one thing for yourself everyday.
As far as the drinking, there is nothing you can do about it. It is absolutely eating me alive. Even if my H and I R, we still have to get over that hurdle. But you can't someone with any sort of addiction (including affairs), if they don't want to help themselves. That usually doesn't happen until they hit rock bottom.
Hang in there. We care here. DO SOMETHING FOR YOURSELF! I have yet to do that today myself, besides getting some crap done around the house... I don't think that counts.