I'm suprised why so many people are saying to just forget about the girl. I dated girls in high school and ALL of them were my friends before. Not just classmates that I got along with or anything but actual friends. If you don't enjoy your self to the fullest, take some chances, and god forbid do something stupid every once and a while you will have a ton of regrets!
And basically the way I see it, your friend crossed the line when he asked for Julia's friend to invite Julia to go to the movies but refussed to have you go. So I wonuldn't even worry about that, plus it sounds like she really digs you.
Also I HIGHLY doubt one of you will screw up the relationship so bad that you both find it impossible to remain friends. But chances are good if you do nothing you will just loose contact with her anyway like most of your friends when everyone graduates.
I just have a hard time seeing (or reading) a situation like this when its really not that big of a deal and you will regret it if you don't go through with it.
I myself finally got enough courage in the beginning of my senior year to ask out one of my best friends. It was just like your situation. I knew she liked me and I liked her but she was afraid we would screw up the friendship. I said lets just try a few dates and see how it pans out. If it doesn't work it doesn't work...
Were getting married in June.