I don’t think you can love someone and cheat on them, sorry. Many couples do stay together after infidelity, but I’ve yet to hear of any who are genuinely happy and get the level of trust they had, back. It’s still up to the OP to decide, of course, but I think staying is going to hurt him more than leaving in the long run.
What you say about people raising/loving their non biological children is true, nonetheless. But obviously it’s the circumstances surrounding the child here that will be the biggest issue.