No, it is not OK. It is unacceptable and too risky.
I do, however, have a male friend I have known since high school, but I do not think my fiance' would have a problem with that, because this guy-friend of mine is gay.
You have every right to be against it, and he should be very understanding about the fact that, of course it is going to make you feel nervous, insecure, very confused, and scared. Your feelings are normal.
I am sorry you are going through this. I take it he has no interest in giving up his female friends or at least putting strict limits on their interactions with him, (like only doing it when YOU are there too), in order to ease your mind and make you feel better. A decent, loving, mature man would do everything in his power to keep you from being upset and hurt, and turn your emotions around, into making you feel loved AND secure. PERIOD! No ifs, ands, or buts about it.
Men are supposed to be protective over their women, and that -includes- protecting our emotions from worry, anguish, confusion, fear, and all other bad things.
You say he is a liar and was caught-out. That is very bad, obviously. I am so sorry for you. I think if he takes your relationship seriously and cares about you, he will agree to:
1. Set new terms that YOU are comfortable with, regarding his interactions with his female friends. Or, ease up and phase them out of his life, for the sake of your peace of mind. He needs to do what is best for YOU, and in YOUR best interest. A good husband puts his wife FIRST. Just like a good wife, puts her man, first.
2. Marriage counseling. If he doesn't like your point of view, then you have a big, big problem that needs to be worked out.
Again, no it is not cool he is doing that. Yes, you have the justified right to complain about it and insist it stops.