Grillinfredd,
Welcome to MB! Sorry you have to be here under the circumstances, but it is a great place for experience & support.
Only you can decide if you want to give him another chance. However, as for the "conditions" to take him back, here is what "WHEN THE ONE YOU LOVE WANTS TO LEAVE by Donald R. Harvey" has to say...
There's a chapter near the end about spouses who want to come home with lists of appropriate reasons to return, and inappropriate reasons that I think is right on target. It is written with the WS being a WH, so swap the pronouns/genders for your sitch.
Appropriate/right reasons:
-Definite resolution of the motivation that prompted the departure in the first place.
-A genuine desire to work on the problems in the relationship (this includes those problems created by the separation).
-A genuine remorse for the pain caused by the separation and a recognition of the need for forgiveness.
-A genuine acceptance of the personal role played (contribution) in the deterioration of the marital relationship.
-In the case of repetitive irresponsibility, demonstrated behavioral change over time.
Inappropriate/wrong reasons:
-Personal loneliness yet having no real desire to be with the rejected wife.
-Purely logistical considerations such as needing a place to stay, financial strain, or personal convenience and comfort.
-Not attaining whatever it was that motivated him to leave in the first place, yet also failing to resolve it (still has the "pull" to the other woman or the "push" of feeling trapped in the marriage).
-Wanting to come back for any reason, yet being unwilling to deal with the relationship. "I'll come back if we can pretend it never happened (avoidance). We can just pick up where we left off."
-Any reason that does not include acceptance of at least part of the responsibility for the marital failure and recognition of the need for forgiveness as opposed to blaming.
I highly recommend Marriage Builders marriage coaching (the # is on this site, it's $185/hr but worth every penny). Also, other books about A's like W. Harley's "Surviving An Affair" and Janis Abrams Spring's "After the Affair" helped us.
Recovery is possible, but you both have a lot of work ahead of you. Learning to meet each other's needs and re-working bad ways of communicating isn't easy. Hope this helps for starters. Move slowly, he messed this up by cheating, and you need to give yourself time to decide what you want to do. I believe it's Dobson that says you never have more leverage than after the discovery of the first affair to set things right. Use this chance!
MSA