Oh man. I'm so sorry you're faced with such a difficult situation. I am pretty sure nothing I say will help. I can only hope that with sobriety and some time your husband can learn to forgive you and maybe stay together if the marriage can be repaired. If the marriage can't weather this hopefully your kids are pretty young. My ex and I divorced when my daughter was 2. She just doesn't remember things being any different. She actually likes that we're divorced....says it creeps her out to think of us together
We are friends now and have always kept our issues away from our child. She just sees that she gets two of everything and the complete attention of the parent she is with in the moment. But I do hope you can fix your marriage, if that is what you want. But trust is absolutely paramount and if that can't be restored the relationship will have lots of resentment....and that is miserable.
It will take time for your heart to heal. But it will heal much more quickly if you are sober. You can do this!