Interfacing is awesome. If you can't find a good interfacing, a couple layers of muslin or broadcloth, or a single layer of say, a thin twill or denim, usually will do the job. The goal is to take the strain of the seams off the fashion fabric, which tends to be more delicate than a tightly woven cotton of some kind. You do what's called flat-lining, where you just stitch the support fabric to the back side of the fashion fabric with your stitching in the seam allowance (eg at 3/8s if your seam line is supposed to be at 5/8s) cuz then you won't see the stitch line when you sew it all up. Then you treat the supported waistband exactly the same as you normally would.
Your dress sounds really cute, by the way! I hope it turns out the way you want