As the others have said, step one is counseling for you. You didn't cause your husband to be unfaithful, and you certainly didn't cause his drinking. You need to really believe those two things to be in the right frame of mind to get through this process. Please call someone and make an appointment today.
It sounds like the two of you haven't done any marriage counseling, even after he was unfaithful? After you start counseling for yourself, you might be able to see if there is anything worth trying to salvage in your marriage or if splitting up is really the healthiest choice for all of you. A counselor can help you to determine that - it sounds like divorce may be the best option but you want to be sure before you go through with it. If you haven't reconciled yourself to the fact that it's the best choice, you may end up beating yourself up with thoughts of "if only he went to AA, then we could still be together" or "if only we did marriage counseling" or other "if only" thoughts. If you're prone to that thinking, then go ahead and throw those options out there. If he still refuses to do any work on himself or your marriage, there's your answer. But you can rest a little easier knowing that you tried everything. Again, if you know in your heart that there is no love and nothing to salvage, then move ahead freely...I just know that I'm an "if only" thinker and had to exhaust all options before being comfortable with divorce. And I waited way too long and put way too much energy into that, so don't be like me :-)
While you're working with a counselor on your emotional needs, you'll have to deal with the practical side of things. Get referrals to three attorneys and set up consultations with each of them (which should be free or at very little cost to you). Hear what they have to say, take good notes, and decide if one of them sounds like the right person to work through the legal side of things. Meeting with an attorney doesn't mean you have to file tomorrow, but it can give you a good sense of what your financial and child situation will be given your circumstances and state laws. You'll have a lot to sort out in terms of financial support, child custody and visitation, division of property, etc. If you're in a strong frame of mind and he is being reasonable, you can consider mediation, which saves a lot of money. If you know he's going to take advantage of you, though, plan on litigation.
Know that lots and lots of families go through this and come out all right in the end. You will too. Take care of yourself and your children. Keeping things as stable as possible for them depends on you taking good enough care of yourself to be strong and healthy through this. Rely on your family and friends for support, and get into counseling ASAP so that you can push past your self-blame. Go straighten your crown and hold your head high. You've got this!