First of all - take a deep breath!
I can relate...now, I am not pretending to be a counselor here. I am only sharing my own thoughts...and gosh, I hope I can help you a little bit.
Please keep a few things in mind. You are not responsible for his actions. You are not at fault. He has a problem and he needs therapy.
He can (probably has) make all kinds of promises that he'll never do it again, but without help from a qualified professional, it's as futile as a diabetic promising never to have high blood sugar again! It's a disorder... a deep seated compulsion. Please read up on it and empower yourself.
It does NOT mean he is a bad or harmful person. It does NOT mean he is a PERVERT. He is a human being who has likely been living with shame based issues for a long time. But he can be helped. You can too!
I bet you're feeling pretty betrayed, hurt and confused right now. But I'll tell you something, this problem coming out can be the best thing that ever happened to him. Now he can get help...now he can learn to live and deal with his stresses and problems free of shame...and with time and therapy you can have a better, more honest relationship.
Please be kind to yourself. I don't think you mentioned whether the law was involved. I'll tell you, with our case they were - and thankfully, it scared the daylights out of my husband, and gave me some leverage to insist that he either get help, get serious about it, or get out. Thankfully, he chose to get help.