It's obvious that you haven't gotten over him yet and cannot be "just friends." He knows this. Thus, he's not 100% true to his girlfriend when he contacts you. (Does she know?) Particularly since you were the one to break up with him, he's simply trying to make you jealous.
The best thing for your mental health is to tell him that you still have some unresolved feelings for him, and because you respect that he's in a committed relationship with someone else, you're going to have to stop talking to him right now because your feelings are still a little too raw. Tell him you have a hard time being "just friends" with him right now, but at some later point when you've had more time to get over time, it may be easier. Don't continue to play games with him. Your candid admission may win him over, who knows.