Marriage & Cheating.

Ive been married for 4 months and since I've caught my husband talking to other women online, in a sexual way. He says he sees nothing wrong because it's all anonymous and nothing big. Yesterday made it the second time, I found dirty emails between women on craigslist, and posts ("Married man looking for a hookup"). I don't want to give up on my marriage this soon but I don't know if I have it in me to deal with this again, just wondering have any of you ever dealt with a cheating man, stayed and had it change?