<human>: Can you succinctly summarize the text in 1-3 sentences?

Back story: It's an open marriage... with definite rules. Before we got married he fooled around with someone who was out of our rule perameter. He claims the rules were fuzzy, but he knew what he was doing wasn't right, which is why he hid it for so long. Eventually it came to the surface. It sucked, but we found a way to make it work, promising to root our new beginning in honesty, and making the rules very concrete and known. 

After the dust settled, I asked him to cut ties with her. He agreed it was a good idea, but didn't actually do it. Texting continued whenever he was out late drinking...(can't lead to anything good in my opinion). Some texts were suggestive, others harmless. I have no idea if any of them led to sex. 

So obviously I can't exactly confront him about the continued contact, because I'm a shitty snoop that went through is phone (I know, I know). So instead I contacted *her* and asked very politely if they would cut contact. She is a reasonable person and completely understood my side. She agreed. 

Yet the messages continue. Especially when either of them are out drinking. Which to me signifies that they're doing this as a prelude to hooking up again. I asked him again if they ever 'talk' and he swore to me they had no contact. So he's lying to me again, which breaks my heart. I am usually a trustworthy person, but I've found myself now doubting everything he says, which can't be good. And I've reduced myself to a text-reading snoop, which is also lame, but I'd never know he was lying otherwise. 

Perhaps their messaging IS innocent, but even so... it is so inappropriate. Am I really crazy to think remaining friends with the person you cheated with is inappropriate?? Am I overreacting? Can I ever trust him again? If so, how?
<bot>: husband continues to text (and lie about it) the girl he cheated on me with. What can I do?