Thank you for bringing your question to Just Answer!
I would not advise telling his boss about the affair. Managers get very defensive when someone who is not employed by them tries to communicate. It could even make the boss decide to fire your husband, which would put your own financial situation in jeopardy.
Hopefully you will bring this up in the counseling sessions and your husband will decide to transfer her to another part of the company so they don't have to interact.