Your husband says to you that he will never cross that line but...he has already crossed the line. When I was growing up my Father used to say that married men and women should not be friends with someone of the opposite sex. I always thought he was crazy and old fashioned but with more years, and therefore more experience, I now realize he was right. The truth is that when a married man and a married woman become friends "outside" of their marriage, they are asking for trouble.
If everything is on the up and up why did your husband lie about talking to her? I think the answer to that is that he knew he was in the wrong. You also state that she had an affair with his buddy and she lied to you about knowing your husband. That establishes that she is a liar and a cheat. Not surprising, since lying and cheating always go hand in hand. If we are defined by the company we keep, what does this say about your husband? I suggest you let your husband know immediately that he already crossed a line and insist that this "relationship" ceases.
Bottom line here...your spouse should respect reasonable boundaries, which he is not doing. Ask him if friendship with this person is worth his marriage.