I see no one (including myself) has provided a link for you but I do remember this topic. What I would do...determine what width biding you wanted to use. Sew opposing fabrics together with strips opposing to reduce wavering/wiggling of your fabrics. Press seams open; press binding wrong sides together to make sure you have your binding as close to perfectly aligned as possible. Then stitch to top side of quilt and wrap to back. I hand sew my back-side bindings so that is what is what I would recommend to be able to control exactly where the front/back of the binding falls. But that is me.
I did do a quick search of 'two color bindings' and got nothing quickly accessible on the site regarding this subject. Perhaps you could do a more in depth search and get different answers??? Good luck. It sounds like a really awesome concept for some quilts and one I may try myself at some point.