Yes you can!
It takes some fiddling with the measurements and then stitching to get your seam to land right on the fold between the back and front.
Here's a link that I keep to help me when I do it. I don't keep to their measurements, adjusting according to how wide of a binding I want to have showing. I do a trial run with some scrap fabrics, until I have the look I want and then go for the actual ones I want to use.
http://www.instructables.com/id/Two-Tone-Quilt-Binding/
But it can be well worth the effort and really makes for an impressive finish of a quilt.