Her not loving him doesn't mean that she was over with him. She didn't give herself time to heal herself. And got into a relationship with you too soon when she was obviously not ready. It was really selfish of her to accept a relationship with you when she is still stuck on an ex. I'm guessing you don't really have much relationship experience. So take this as a lesson and don't do this to yourself again. End the relationship. Not just for you but for her too. She needs time to figure out her problems or she might just find another rebound guy.

She is emotionally investing to a guy that is not you. Yeah i would be jealous too. Her talking to a guy she likes is not good at all. What if she falls for him or she already has and doesn't want to accept it?

Yep 3 months is too soon to try to be friends with an ex. Her feelings for him are too fresh. Also, why you decided to put yourself in this situation? You are obviously the rebound guy.