I'm sorry to hear this. It's a shame whenever it happens. 💔 I have two suggestions, though I suspect you're not going to like at least one of them.
A. Go to counseling without him. Use the time to sort through your thoughts and emotions. A counselor's office gives you a safe place with somebody trained to help you through the process.
B. This will sound cold, so I'll apologize for that in advance. Move on. Staying in a bad relationship "for the kids" very very rarely works out, and you (general "you" not you specifically) end up regretting it, or worse resenting all the time you lost. More importantly, kids are observant. They'll almost certainly know something is wrong. And whether they do or don't notice, think about what sort of relationship you're modeling for your kids. Presumably you'll want them to have happy, healthy relationships when they're adults. One of the best ways to help that happen is to show them what a happy, healthy relationship looks like. And "staying married for the kids" is not an example of that.
Now, that said... by all means take my suggestions one step at a time. Keep seeing the counselor and let him/her help you work through everything. I suspect you'll come to the conclusion that moving on is in everybody's best interests - yours, of course; but also the kids and even your husband.