Rachel, Yes to third party! Do you have an older couple to help? Even an older man/father figure he trusts? Keep loving him. It's not your job to fix his unhappiness. He went the wrong way & needs to change.
I have held my peace for this long because I, too, hate confrontation, but can we stop the blame train for just a minute? Do you think it possible that he has, in reality, done nothing wrong?
I have a feeling that if Rachel does get a knowledgeable third party involved, she may not like some of the things the third party would have to say to her. She is the one who has labeled this friendship inappropriate. She is the one who has decided that he was cheating in his heart. What was it 3goodeggs said about communication? Rachel's husband has said that his feelings toward this woman aren't any different than he has had for any of his other friends, and that he is being punished for something he didn't do. Rachel has said, in effect, "I don't trust you; you are lying about your feelings for her," do you suppose maybe he actually knows what he is feeling, and has been telling the truth?
I'm sorry, but I must disagree with NorthFLChick - I think this is jealousy. There are two kinds of jealousy; jealousy with cause, and jealousy without cause. Jealousy without cause is blasting a guy for just making eye contact with the waitress at the restaurant, and jealousy with cause is catching him excusing himself from the table to get her phone number.

Rachel, honey, I understand that you would be feeling powerless and vulnerable at this time. Seeing your husband spending this much time and attention on this woman could make you feel even more exposed; that's understandable. It is your husband's responsibility to do what he can to make you feel safe, not more vulnerable. If this friendship made you feel threatened, he needed to do whatever it took to remove the threat, and if ending it was the only thing that would work, that is what he should be prepared to do. But let's face it, if this was another guy he was palling around with, we wouldn't be having this conversation; you'd be glad he had a fishing buddy. Telling him that this friendship of his made you feel scared and vulnerable was the right thing to do; he could then see what he could do to make you feel more secure. That's treating each other with the respect that adults deserve.
But however powerless you might be feeling, everyone in a relationship has power, and it must be wielded with care. When you confronted your husband, you took the power that you have, balled it into a fist, and hit him over the head with it. You put him in the position of having to tell this woman, "I'm sorry, but my mommy says I can't play with you any more." Is it any wonder he feels resentful?
All friendships, even same-sex ones, are like little romances - you see something you like in the other person, you enjoy each others' company, you share common interests, you feel each others' joys and sorrows. Whether there really were romantic overtones developing in this friendship I cannot say; I am clean across the country, and I am only seeing it through the filter of your perspective. But you have hurt him badly. However necessary the ending of this friendship may or may not have been, by forcing it on him the way you did, you have driven a wedge between you and your husband. Honey, it's now your responsibility to see what you can do to mend those fences.