My first question would be, do you have children with your husband?
I am a male who at one time had a friend go through this ordeal. If you want to continue your relationship with your husband, and you have children, and you are quite sure this will never happen again, forgive yourself, get sober, and don't say a word. It can be a secret.
If you have no children, and are unsure of your relationship with your husband, and need to fix other issues in your relationship let him know, but be ready to be divorced. Each man is different in regards to handling this kind of news, but most, especially if you have no children to look out for, will leave immediately. If there are children in the equation the dilemma changes and could ultimately become the burden of the children.
You know your husband best, and for my friend, it was one of the most difficult things he had ever heard. If no child was involved he would had left, but he decided to stck with the marriage and make it work. But many men are not as understanding as he is.
I will tell you it was the most unimaginable, most painful news my friend ever heard, and I still don't think he would ever really trust his wife again.