Wow, TO, that's a lot!
I totally agree with 25- that woman is way beneath you. No more talk, contact, anything with her from you. Let her be on the low road. You stick to the high one.
I know how hard this will be for you to do this- and others may disagree here.... but I think your best course of action is (again, I know this will require you biting your tongue in half) to drop the whole discussion with H.
He is obviously not being honest with you about communication with other people, but I don't think bringing it up to him is going to change that for the better. It hasn't in the past, has it?

Can you take yourself back to that place we went months ago, when I told you when you get tempted to talk talk talk to him, and need to just be quiet, to picture all of us peeking into your kitchen window saying in a hissing collective voice, "T0!!! STFU!!!!" At the very least, get a good laugh out of that visual. I just did. We could all probably use that visual, come to think of it. And I'm going to start with ME! LOL. Hang in there.

M-60 H-51
M-14 years
BD 12/26/16
S 1/1/17

"First the pain, then the rising."
Glennon Doyle Melton