Jealous over baby?

I have this cousin who has a one year old he loves his baby to death but it seems like his girlfriend is really jealous of that. She gets really mad if he pays to much attention to the baby and not her. She threats to leave and take the baby with her for no reason. Are there people who are jealous of their babies? Is it normal? I’m 7 months pregnant and my boyfriend kinda sends of those jealous vibes with little comments.