Hi Batgirl,
You process it by taking it one day at a time. Yes, it hurts to see someone that you love so much act the way they do. Is this the life you want. Him lying, cheating, and manipulation of you. That is not a healthy relationship. There is nothing you can do for an alcoholic to cure them. I'm sure you have read about the Three "C's" You didn't cause it, you can't control it, and you can't cure it. I know you offered to be their with him to get him through this. This is his journey. He will either do it or not.
Your Heart and your head are battling over this. The heart does not want to let go of this love. It takes it a lot longer for it to come around. Your mind knows what it should do, but gets confused by what the heart wants. Know that with each day it will get better. You are strong and can get through this.