I agree with Webgoji, that your h, needs to at least, acknowledge how you are feeling, in regards to how you have been treated. It doesn't happen, in a vacuum. I'd err, to suggest, that perhaps, not so much jealousy, as feelings of being unheard and unsupported in your 'feelings'.
To request, 'never' having any contact at all with the woman he grew up with, his sister, seems like quite a hefty demand. His connection to her, isn't a reflection of his feelings towards you.
Has he ever, once, said to you, I can see how my sister can rub people like that? I can see how you might feel that way? And come up with suggestions on how to take her, or to at least sit down with the two of you, to try and resolve this? It would seem hard, to distance from a niece. Hence, it being even more of a tough demand. And even, if he cannot get the two of you to like each other, at least he needs to acknowledge your point of view, as valid. Acknowledging your point of view as valid, and remaining in contact with his sister, isn't dismissing his feelings for you.

Hope you can both, work through this. Stuffing emotions, can have future physical health consequences.