Best to just say "I know all about you and ________, so please don't disrespect me or our family any further by continuing to lie about it." If he does (lie), then put your hand up in the "STOP" position and -- looking him straight in the eye -- say "Stop it. We both know you're lying to me right now, and it's incredibly disrespectful not only to me and to our marriage, but to our family. We always taught our kids the importance of honesty; I've decided that WHATEVER happens with us, I am going to insist on that in our family moving forward." And then if he persists in the lie (ex.: "we're just friends"), turn and leave the room.
I had to do this with my wife. From my personal archives:
Boundaries/”Start with the DECEIT”
I would start with the DECEIT.
Once it became apparent in my sitch that my wife wasn't going to end her affair, despite confrontation, exposure to her parents, siblings, our adult children and her employer, I decided that I couldn't stop her. But I was DAMNED sure going to stop tolerating the DECEIT. She was lying to her own parents (whom I love and respect, very much, and who have been like PARENTS to me throughout our marriage), and to our adult daughters.
So my BIG boundary was this:
"I will no longer tolerate your deceit. I will no longer stand idly by while you have an affair with a boy half your age, and then not only LIE to your parents and our children about it, but you make wild accusations about ME, that I'm 'crazy' and paranoid. Well, that's over. You either tell them the truth, or I will, and I will show them the evidence that I have. You have exactly five minutes to decide."
And I was dead serious.
btw, my smaller boundaries were:
-- no calling or texting OM from inside of our marital home;
-- no calling or texting OM in front of our kids, regardless of where you are;
-- I will no longer allow our family's finances to be spend enabling your affair; you will have to get your own cellphone, and pay for your tummy tuck Visa payments, lingerie, hair-coloring and what-not.
-- If you plan on coming home after 1am, don't bother coming home.
In your case, since you're living apart, I would start with the DECEIT boundary. It's incredibly disrespectful, and there's no reason why you have to stand there and be lied to, continually.
"What is best for my kids is best for me"
Persevere = happily being patient over a long period of time