SPOILERS AHEAD: NO CONSISTENT INTERPRETATION
SPOILERS AHEAD
There is no consistent interpretation of this film. If they were married, she would not have had to tell him how far it would take to drive to the small town, or that she had a car, or all the facts she mentioned about her sister. If they were just play-acing in the second half, he would not have gotten so angry at her. If he was the father of the child, as one poster has suggested, and was visiting Italy, he would have made some effort to see his son. He did not know his way around the town where they supposedly had spent so much time together. I think you have to accept this as a surrealistic film and not try to find a consistent interpretation which would make all the pieces fit.