the post by John D isn't true, they aren't referring to James as the "he", although yes, James is the father of Lily and Ambrose.
in the time Kathleen knew her, Rose considered herself to be a female. However, by the end of the novel, he has chosen to identify as a man. this is why he is referred to as a male / 'he'. He dresses and behaves like a man, and considers himself to be one. this is just a further step to the already "manly" or butch way he acts when he is around Kathleen in the time they are in NYC together. one could say he is transgendered or transsexual without having undergone an operation.
i know this thread is old, but i just wanted to clear that up.