My wife has a male friend whom she texts, e-mails, Facebooks, or talks to every day. She says it's a normal friendship and I shouldn't worry about it.
I notice she talks to him only when I'm not around, usually when I am asleep or out of town. Is it normal for a married woman to have a relationship with another married man that entails that level of sharing of small details about their lives, or am I making more of this than is there (what she says)?
Answer: It's an automatic alarm when someone pushes responsibility back on the person who expresses concern.
Innocent friendships do happen, but they find their way into the open; you would know the guy, or you'd be able to read over her shoulder as she typed, if you wanted to - and, likewise, you wouldn't want to, because she'd just be typing to a friend. She'd do things like leave open a half-finished missive while she went to the bathroom or answered the phone.
Unless you have a history of chronic jealousy (which would necessitate a whole other answer), she's failing to show you the natural respect felt by someone with nothing to hide. She'd say, "Wow, I'm sorry - no, this isn't some kind of illicit friendship," followed by some factoid about the friendship that made inherent sense, like, you just realized you have a friend/school/town in common and you were just having a running catch-up session. Or even "He's a great friend, and I find it easy to talk to him, but I have no ulterior motives - and maybe I am giving him attention that I should be giving to you."
Short version: Her furtiveness + defensiveness = her having some explaining to do.
What you do now is harder to piece together, but I think your best bet is to create an environment conducive to coming clean (for both of you): Without anger, sit down with her and say you believe you've earned her respect, by having a history of not being jealous or making baseless accusations. Then say you didn't object to this friendship of hers lightly, and you would appreciate her taking your concerns seriously instead of deflecting them back at you.
The most important thing you can do to create a truth-friendly environment is to make it clear you're not going to yell or scream or punish her for telling the truth. Just say you'd rather hear the truth about the friendship than be left to wonder why you have these uncomfortable feelings that something is going on, and why she doesn't want you to express them.