Hi, I'd like to help you with your question.
It sounds like from what you described that your husband has a lot of emotional issues to work through. You can have problems in a marriage but no matter what happens, it should not cause an affair with someone else. Nor should the partner having the affair blame the other. The person having the affair is solely responsible for their behavior. He broke the trust in the relationship and that needs repaired, by him.
You mentioned he has trouble with feeling anything towards you or the kids. He also has a lot of anger. Has the therapist you are working with helped him explore any possible childhood issues that could cause your husband to withhold his feelings? Any abuse or neglect in his background? Also, inadequate parenting, such as a parent who is emotionally unavailable, can have a great effect on the kids. Is it possible your husband experienced this in his childhood? That would explain how he is reacting now.
It is good that your husband was checked out physically. Often, therapists refer patients for a physical before considering behavior to be psychological. This way, you know his issues can be dealt with in therapy.
It is possible for your husband to regain his feelings towards you but he needs to work out his issues first. The therapist should be able to help him with that, but he could also see someone on his own too.
There are some resources that can help you. One is http://www.5lovelanguages.com/. They offer great ways for couples to learn to communicate with one another. Another resource is After the Affair: Healing the Pain and Rebuilding Trust When a Partner Has Been Unfaithful by Janis Abrahms Spring and Michael Spring and Communication: Key to Your Marriage: A Practical Guide to Creating a Happy, Fulfilling Relationship by H. Norman Wright. You can find the books on Amazon.com or your local library may have them for you.
I hope this helped you,