I would strongly recommend that your husband write a "no-contact" letter, the content of which is to be approved by you, and it is to be DELIVERED by you, to the OW. You also need to set up a transparency system, whereby you can feel comfortable that they are no longer in contact. Change his cell phone #, with detailed billing on the new #, and the bill coming to you. He leaves his cellphone out. You exchange daily schedules.
I do think your husband is sincere. I also think he won't be able to pull it off without a system in place, as his past history makes him a very good candidate to backslide.