Depends what your STATED boundaries are, and what evidence you have. If you've let him know that you won't live in an open marriage, nor tolerate deceit or the disrespect of him coming home late if he's been with OW, then get proof of it and take a stand.
Locksmiths can be of great help.
I would wait until one of his waltzing in's is a late at night one, and you have solid proof.
Another thing you can do is ANYTIME he lies to you about his affair, and you have proof, just STOP HIM. Put your hand up in the "stop" position and say "Please STOP IT. We both know you're lying to me right now, and it's incredibly disrespectful. I can't stop you from having an affair -- you're an adult, and YOU'LL have to live with that choice -- but it violates my own personal integrity to stand here and listen to you lie to me about it."
