Your description of this series of events is what we call an emotional affair. It is just as damaging as a sexual one. Change is difficult when one partner won't go to counseling. It is difficult to process such behavior when one person won't allow for real disclosure. One option that is pretty new sometimes allows one partner the anonymous quality that makes them more comfortable - they do not have to be seen. Online therapy is quite popular now and can be done without actually visually seeing the therapist. Of course web cam is an option too. You can schedule appointments while you sit in your living room. This sometimes can nudge a person towards giving therapy a try because it has this almost anonymous feel.
If you find that he is still resistant then you have self help but that too needs his participation. My favorite guide on communication is the Mars and Venus series. You may see progress if communication is addressed. Maybe there was some reason why he sought this affair but you have to find out what that is. Finding the reason is key to resolving whatever led to these choices.
You can also find some guidance in people you know such as your priest or pastor. If you meet resistance in all these efforts then he may not be open to resolving this and that is a red flag. I would approach him with these options and tell him that you need to get past this - with his help. He has to feel that you need his help so that you understand it. If he won't talk then nothing will change.
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