First off, this is a horrible situation to be in and I hope you can sort it soon and make peace

Honestly, I think I actually would get in contact.
It's all about how you do it though, like you said, she could lie and even if your Husband is saying "Go on then, ask" that could either be an honest "Nothing's going on", a bluff or confidence that this other chick won't spill.

It's been a few years since she tried to get back with him during the start of his and my relationship but it doesn't mean I don't still feel pain or irritation whenever she calls or texts (If it's just work, I can bare it) but recently she texted AND called (Because he didn't reply straight away) while we were having dinner about something non-work-related. After the call, we talked about it which then turned into a full blown argument. It just never ends.

This was my plan that I didn't end up doing simply because my other half actually went to her and told her off and said she can't be calling if it's not business, told her I didn't like it and she was embarrassed and sorry so I'm over it for now but if I ever find myself in the same situation, this is what I was going to do and what I will do.

Get her number, either off of her if on Facebook or ask him, since he's so okay with you talking to her, keep it lighthearted though, you just want to talk and who knows, you might get along and find a friend in her. "If she's apart of your life, she's apart of our lives" and that's NOT unreasonable, just incase there are any arguments back that make you doubt yourself.(Even though in your case, it seems like he's okay with it)

Drop her a friendly enough text asking to meet up for a conversation. Grab a coffee and go for a walk in a nearby park or something. Try keep it light at first, how's the new job etc. and then just be real with her and don't sound attacking at all, that'll pull her back, if she doesn't like you, she may not want to tell you anyway because you would have made her feel like something bad's going to happen to her "Look, I know this might be a little intense but I've had reasons to believe that my husband may not be being truly faithful and I just need to know" Use words that bring her into it so she can relate. None of us want to be cheated on, a lot of us have been and that feeling is truly sickening and demeaning. You don't want to waste more time that one already does with a cheater. Maybe she hasn't done anything but maybe he has been very flirty either with her or others which is still something you must talk to him about, because it's not acceptable, a small amount of flirting maybe if it can come across as charm but not if it's increasing to the point where he's just a married man, acting single. (Look up the right way for that as well, the wrong words can just push people away and you'll never resolve it).

If something has happened, then you know and it's really up to you what you do from there, I would suggest not taking it out on her but I don't know what this woman's like, she could be nasty and rude but even that could just be a defense mechanism so try and always be kind.

If nothing's happened and she doesn't know about anything else or anyone else, thank her truly. She may want to help, remembering how lovely you were, if she ever hangs out with him and other friends.

Communication and the right words and energy are key, there may be nothing going on but there's definitely something in the relationship that isn't being addressed, he's not making you feel loved I expect but the viscous cycle is that you may not be doing a good job of making him want to make you feel loved if he's feeling nagged or untrusted (Sorry if that sounds harsh but everything that's worked in my own relationship has been the ability to look at myself and change something that was making me unhappy that then put the relationship at risk)

I hope something in this helped, so sorry if not. I really hope this works out whatever you decide to do. Certain things like even flirting increases if left alone, it's got to be nipped in the bud every time or it'll grow until the worst possible thing happens and that's your relationship broken. All the luck in the world to you!

Personally I would keep it between me and him. Until I have solid proof I leave it alone, but if the proof is found or if you're intuition is coming at you harder than you can stand, it may be best to leave the situation or do a grand gesture to feel that connection again and move past it. This good read helped me rejuvenate my love for myself and eventually my fiance' through a very rough patch in my relationship and now we're getting married this summer. http://tinyurl.com/her12sweetwords Best wishes to you.