Hi, I'd like to help you with your question.
There is a difference between physical cheating and emotional infidelity only in name. Cheating is cheating. It is undermining the trust of the relationship which is needed to have a good relationship that works. Without trust, there is no relationship.
There is no such diagnosis as Bipolar infidelity. A person can have Bipolar and cheat due to the manic phase of the illness. It can cause sexual promiscuous behavior that is hard to control. But medications and therapy can help control those symptoms.
If your husband is cheating and has Bipolar, he should be in treatment if he is not already. He can get an evaluation through a trained therapist. They can help confirm a diagnosis and give him treatment options. For most people with Bipolar, medication is necessary. Bipolar is a brain chemical imbalance and cannot be helped by therapy alone.
Even if your husband has a good reason for his behavior, that does mean it hurts you any less. He needs to acknowledge your pain and start to repair your relationship. Here are some steps that need to occur:
One, is your husband sorry for what he did? This is important, because if he does not take responsibility, recovering your marriage will be difficult.
Two, has your husband stopped all contact with this other person or people? He must do so as a first step to regaining your trust.
Three, has he done anything to start repairing the marriage?
Four, are the two of you talking about what happened? Your husband needs to be open and honest about what he did and let you ask any questions you need to. He broke the marriage vows. He needs to own up to it, illness or not.
These are some of the most important issues you both need to be working on. Talk with your doctor about a referral to a therapist. If you attend church, talk with your pastor. Pastors are often very good marriage counselors. Also, if you have problems affording therapy, try your local community mental health center. They can offer therapy on a sliding scale fee system.
The main issue is to rebuild trust. It can take a while and a lot of work, but you can do it as long as you both are motivated.
There are some books that may help you. One is called Infidelity: A Survival Guide by Don-David Lusterman. Another is Not "Just Friends": Rebuilding Trust and Recovering Your Sanity After Infidelity by Shirley P. Glass and Jean Coppock Staeheli.
You can find these both on Amazon.com or your local library may have them.
This is painful for you and you need time to recover. If he will not work with you on this, see a therapist yourself. You need the support right now.
I hope this has helped you,