There isn't some "unwritten rule" like there is between a guy and a girl. If he surprises you by taking you out, he would normally pay. If you decide to go somewhere together, you might split the bill.
One of you may be much better off than the other and decide to pay for the whole thing.
As far as personal experience goes, I tend to just stick with drinks (alcoholic or coffee or whatever) that way it's easy to either take it in turns getting the rounds in, or you could simply pay for each other's drinks.