Uhhh... if it walks like a duck and talks like a duck, then your husband isn't being honest with you and he's trying to deflect and make you look like you're paranoid. You're not being paranoid and that is not a "friendship."
In many situations I do think it's possible for men and women to remain friends, but in this particular situation I'm not sure that that's true. I couldn't tell you with certainty one way or the other. Sure he's being defensive and trying to turn everything around back on you in spite of highly suspicious behavior. If he's not cheating, then he can't prove a negative. And the man code is always deny deny deny. But if he IS cheating then there will be proof, and if it's in receipts, texts, and e-mails you deserve to see them.
He does need to end this "friendship" even if no physical cheating has occurred. He's been spending time with a woman who isn't his wife and spending emotional energy on her that should be with you. He's not willing to disclose anything about this relationship to you and that's suspicious. But again, even if he's not cheating in any way, he still needs to end this particular friendship. The appearance of impropriety demands it. The fact that you're uncomfortable with it demands it. It's a problem friendship because you have a problem with it and your marriage should be more important than the friendship.
If he refuses to end the so-called friendship with this woman then that will tell you all you need to know. If he claims he's ended the friendship and you find out he doesn't, that's another red flag.
By the way, the number of fathers per her number of children doesn't really mean anything or apply to your situation. It doesn't even really speak to her character either. What DOES speak to her character is that fact that she doesn't have any boundaries with a married man and *could* be cheating with him.