I knew my ExW was having an EA (and quickly confirmed PA). I mean I have hard evidence of it. I absolutely knew for a fact. I confronted her several times about it over a couple months, slowly showing her more of my cards and each time giving her the opportunity to come clean about it. (Btw, this is not the approach people on here would recommend and I did this before finding the forum). Each time she would look me in the eyes and point blank/flat out lie to face denying as much as she could. And, I knew based on my snooping she always got off on lying to me and being secretive. My point is, based on what you've presented here despite what your husband is telling you he's almost certainly having an affair with this woman. I know you don't want to hear that, but it's a 99% probability based on all the experience people have here with these situations. It doesn't mean you can't stand for your marriage, forgive him, and maybe work it out...but brace yourself for that eventual truth.
Do not reveal WHAT you know of HOW you know, Only that you DO KNOW.
Here is a good response: "We both know that is a lie (on not true). When you are ready to speak the truth, I will listen" Then walk away.
