It is good that you are talking - that is priceless. It can't erase the past but it can explain it and eventually get past it. You will never know anything for sure. It's up to you to decide how much of what he says you belief and what you choose to forgive. Don't over generalize though. Because he had an affair doesn't mean he even considers he could have married her. You must use this new communication to rebuild and to find your peace again. He is reassuring you so you have to begin to trust those words again. This will take time and patience. I don't think a lot of people really stay for the kids because those relationships can be maintained through a divorce. Most people stay for their own happiness. Consider that when you are thinking of his motives.
If you are going to stay together, give it 100% and find trust again. Find a counselor that you both like and go together. They are out there.
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I am very sorry to hear about your husband's affair, but glad to know you are still with him and want to work things out. Once trust is broken in a marriage it is difficult, if not impossible, for the couple to rebuild trust without professional help. You were wise to see a therapist; I am sorry you did not find someone who could help you. Please don't give up. I recommend that you find a Marriage and Family Therapist to help you through this. MFTs are highly trained to deal with couples issues, including affairs. You can find an MFT in your area by going to http://www.therapistlocator.net . It has been my experience with my couples that affairs can be worked through, healing can take place and a new trust can be built. It will take time, but with work your marriage can even become stronger. I hope I have answered your question. If so, please click on the green accept button so that I will be credited for my professional time. I wish you and your husband healing in your relationship, take care, Eleanor