I've been going through something similar and as you have 2 children you have a very good case for remaining in the marital home with him leaving, but unless he agrees to it you can't do it without going through the courts.
If he agrees you can get an agreement drawn up and signed and he can look for accommodation elsewhere. If he does not agree to this then you have to go through the courts who will put the children's needs first and foremost.
I don't know your financial situation, but mine was very poor in comparison to my husband and so I was told that I had a very strong case for being granted occupancy to the house with him given a court order to leave. In the end I decided that this was going to take too long and cause so much grief that I just gave up and now we're selling the house and the profit will be split (in my favour). I have no plans to divorce immediately either.
His infidelity, as far as I know, is a very strong case against him should you wish to remain in the home and have him, leave. Your children will always be put first in the eyes of the law.
Hope this helps, and good luck.