I am so sorry. Do you have kids with this man?
I have an exceedingly hard time believing this was only a platonic relationship. If it was why hide it from you? Why not invite her over for dinner to meet you, or at the very least (if we want to wear blinders about this) mention the friendship a few times in passing? People don't hide things when there is nothing to hide.
If I were in your shoes, I think I'd call this woman and ask her what their relationship was like. She might just come clean. Did she know he was married? Even if she did she may have her own motivation to share the truth. If she's the kind who knowingly sleeps with a married man, she might be motivated to tell you so that she can pick up the pieces if you leave him. If she didn't know he was married, she might just be pissed and want you to know.
If I were in your shoes, this girl would in the very least be getting a phone call from me. IF she said that they slept together I'd want dates and times that it happened. I'd also like to know one or two things that she would only be able to answer if she had been intimate with him. (That way he won't be able to confuse you later with lies) Other than that, I would try to avoid details, as the more details you have the harder this will be to put behind you.
If the answer is yes, and you are convinced of it, AND you still want to stay with the guy and trust him again I wouldn't do it without giving him one last chance to redeem himself and "walk the walk" as you say. Making sure there was no time or oportunity for this girl to call your hubby and tell him that she confessed, Sit him down and ask for honesty one more time. Tell him you're willing to rebuild the marriage, but "_only_ if it is based on trust from here on out. I have to be able to really trust you to be honest with me, so I want you not to answer this question right now. I want you to think about it very long and hard in five minutes you can tell me; did you ever have anything more than a platonic relationship with this woman?" If he says no, kick his ass to the curb, and hire a good lawyer, you will never have a successful marriage with a this man.
If he says yes, take two valium and call Dr. Phil.
You know I re-read what you said above. Why on earth would he be calling her at 12:45 am?! You don't call friends at 12:45 am just to chat about life. What you do call for is a nookie run if you are a turd cheating on his wife. You said he called her mornings, evenings, weekends, and holidays?!? On just what planet, do you have to be to accept that THIS is a platonic relationship? It doesn't even sound as if it could possibly pass as two people who were having casual sex. It is a serious relationship.
Even if the girlfriend doesn't admit to it I'd give him one last chance to come clean and walking papers if he doesn't.
Well, I'm so sorry to hear this happened to you. Best of luck in whatever you do.
Gardeninginthefog