Can a relationship survive cheating?

Can a relationship work through one person cheating? My fiance was chatting with someone he believed to be a girl wanting to meet for sex. It was a scam and not a real person and he never met anyone in person but I still find it cheating. We have a toddler and a child on the way and I know it's been rough since our son died and he lost his job. He said he'd never actually meet up with someone but I dont believe him. I want to leave but I also dont because I love this man and this is the first time he has ever done anything to break my trust. Can we work through it, and if So, how?

Update: he is willing to let me have access to everything. He does have s porn addiction where he met this girl who was a scam. He is willing to get therapy himself and couples therapy as well as doing whatever it takes to earn my trust. I do trust my fiance. I know him and I know the death of our son changed him for the worst. He feels worthless and I have been treating him pretty awful. We both need help and we want to work on this. My step dad cheated on my mom and they were able to work through it and now have been married 10 years. She gave me some good advice. I know if my fiance doesn't change his behavior I will leave him. He knows this too.