Is it okay to have a secret Facebook account?

You need to talk to him and tell him you think it is inappropriate that he has this in a secretive way. Or better yet, get a facebook yourself and find him in there and add him, then add the girl. He shouldn't be hiding this from you. If he has already done things in the past in your relationship he could again. Confront it on it. He wouldn't like it if you were doing the same thing. He needs to respect you and your relationship. Good Luck.