Hello. My name is Marc. I'm a licensed attorney and I will be happy to answer your question.
This sounds like a very informal situation - mainly because the lease ends so soon, it contains no rent, and her demand for increased rent was made verbally rather than in writing. The simple fact here is that there is no enforceable agreement at all between you, your husband and your roommate. If she wants you to stay and she wants more rent, she MUST do one of two things: (1) renew your lease with an amendment stating the rent she wants, or (2) provide you with a new lease that states the rent. If you sign and stay on, then you will be obligated to pay the rent stated in the renewed or new lease agreement.
In NYC, lease agreements must be in writing. They're not enforceable if they're based on verbal promises. So, even if your current lease was enforceable (which I doubt it is), she can kick you out at the end of the month, or you could move out whenever you want. Perhaps it's best to negotiate some reasonable increase with her. Then, have her provide a new lease with the agreed-upon rent.
I hope I have provided some useful information so that you and your husband can better understand your issues and options. If so, please be sure to rate my answer, since that is the only way I can get credit.
Best of luck to you,