Good morning! I am glad to hear you are holding your boundaries. I know this is HARD.
You may have told us this, but I can't remember: do we know if your husband's OW has a drinking (or any other substance abuse) problem?
There will come a point where we can help you deal with your husband's "I swear I'm telling the truth" statements, but that will come later. For now, you're handling it perfectly, saying things like "I'm sorry but I don't trust you right now," and "Considering how you've already lied, I'm having a hard time believing you right now," etc.
I am glad to hear you are holding your boundaries. I know this is HARD.