No Trust and No Respect- Should I Move Out?

I have been married 5 years. In those 5 years we have 2 children, an early delivery in which a third child did not survive. We are both young at 25 years old and didnt know each other very well before getting married. Everything is getting worse. I supported the family (even while pregnant and giving birth) while my husband stayed home with the kids for years. My husband has now been employed for a little over a year. He is a 'homebody' unless it involves him going out with the boys. I like to do many activities. We fight all the time. He refused to acknowledge our 5th wedding anniversary and he never really got me gifts for my birthdays or Christmases ever. since the anniversary, I started to correspond with people online. I know this is wrong, but I had just been through too much for so little. Besides, he had corresponded with females online previously when we were newlywed and I thought he had no problems with me. I recently discovered a picture of a woman in his phone, that he has been looking at/answering craigslist ads for fwbs and looking at female coworkers' myspace pages. I am furious because I put up with so much from him and now he has the nerve to be criticizing and trying to step out on me. He swore that he never had any ual contact with the women and that he was just looking. He refuses to go to counseling and i don't think he takes my woes seriously. I was not comfortable sleeping with him while all this drama is going on, but he insisted. I have not been happy for a long time, but do not want to face the world with two kids and a failed marriage. Should I move out and begin divorce proceedings?