That is not a bad idea, actually. One of the books I read about the aftermath of the affair (I don't recall which, I read several!) mentioned something like that.
In many cases, in order to reconcile, the wife needed a 'good faith' gesture from her H. Sometimes it was quitting the job where OW was, sometimes moving to a new state, but in some cases, the husband put the home and bank accounts in his wife's name to show he didn't plan to go anywhere, and if he did, he would be leaving with nothing.
Glad he was honest with you about what happened. My gut says I would believe him, that it is over with her. But, I am not you. Good luck hon.