I am a very recently divorced mother to twin boys (almost 3 years old). I've been in your shoes. First get a lawyer! Ask all of your friends for a recommendation. Get a good one. Go for a consulation (most are free). Find one you like and respect. This person will be fighting for you and your rights. Once you have the lawyer and know what you're going to be dealing with (the lawyer can give you the basics of how the divorce might go), you have knowledge and you are protecting you and the kids. That's step 1.
Now you can figure out what you want for your future. Do you want to work on your marriage? Is he willing? What do you want to change about yourself? Then take that to your husband and talk to him about what you want your marriage to be. Divorce is a 50/50 deal. BOTH of you have done things that need to change. Keep the lines open between you and your husband. Don't blame. You are HERE now, ya know? Once hubby knows you went to a lawyer and that YOU will be okay no matter what he decides, he may just see you in a different light. I'm not talking about shoving it in his face, I'm talking about an honest discussion about what you both want. This is YOUR life too. Right now you're feeling hurt and scared (BTDT). Take time to think about what you really want. Then sincerely share that with your husband. You may be surprised. But either way, you are taking steps to protect yourself.
As for the children, yours are young (like mine). Explain it in terms of Mommy and Daddy aren't getting along right now and Daddy is going to live somewhere else for awhile. Both Mommy and Daddy love you very much and you will be seeing Daddy a lot (and then make sure he gets to see them - regardless of the situation between you and him!)
I hope you can work it out with your husband and you don't have to experience a divorce. But if you do, you will adjust. You and the kids will survive this and be happy too! Just don't put the kids in the middle (even if you get mad or he's not paying child support or whatever). They don't need to be involved in that at all.