If the quilt top is not finished, I would try and finish it with similar polyester. However, on the back, if you prefer cotton, you can use cotton for the backing. I only would suggest that you wash the cotton first, as cotton will shrink way more than polyester.
Or as others have mentioned, use a 60/40 cotton/polyester blend sheet if you like.
I would only suggest not combining the cotton with the polyester top because of the difference in shrinkage and color fastness of polyester compared to cotton.