No, don't quit, but let him think that you have. I too have to deal with a OW. Will your H see you at all? Have you read Don Harvey's When the One You Love Wants to Leave?
Do you see you H for business purposes? And do you know anything about the OW? I guess I need to read some more of your sitch.
Yes, M is a commitment for life, but it still sounds like you're blaming him-which you should-but not to him. If you have any contact with him, you need to act like a friend, you need to act like it doesn't bother you even though it's killing you inside. If you could get him to see you on a social basis (there are various ways to get them to want to do this) you might have a chance of winning him back. Have to go now. Hang in there.