Cheater

I just found out that my husband cheated on me when he was deployed. I had a feeling and can honestly say that I do not hate him or anything like that. I think I’m going to leave him... but I now live thousands of miles away from home. I have animals that I won’t leave behind. Honestly, I love him and we’ve been together for so long. I also would have to start everything over. Has anyone had a successful marriage after someone has cheated? Or should I just turn tail and run?