Similar thing happened to a friend, he promised to stop seeing the woman concerned, who probably had no idea of his feelings, unlike your husbands therapist who is probably very aware.
My friend felt let down by the secrecy, his lies and lack of loyalty, and seriously considered leaving him. He was very contrite so eventually she stayed, but trust had gone and only now years later things are back to a new sort of normal, but will never be the same as it was.
Be careful Introvert. Try and talk to someone close to you about this, it helps.