I had some success in tacking the tack with my wife of "Look, I don't care anymore what you think about ME, but I DO care about what you're telling our kids. No matter if we move forward as husband and wife, or as EX-husband and -wife, working amicably to raise our kids, I will NOT allow our family to knowingly tell lies to each other. We've never raised our kids that way, and I can't for the life of me understand why you're accepting anything less from yourself. Either tell them the truth, NOW, or I will, and I will show them the evidence I have."
Within the hour, and after more than two months of nothing but DECEIT, she finally told our adult daughters and her parents the truth about the nature of her relationship with OM.
Maybe if you can take YOU out of the equation temporarily, by saying "Look, I don't care about 'us' right now . . . ", you can get him to call a spade a spade.