machine stitching the binding to the front, folding it to the back and hand stitching it down with an invisible stitch will solve your problem.
i have in the past 10 years tried a few times to machine stitch the binding on both sides. i don't care what anyone says it always looks like crap! i figure if i'm going to put all the work into making a quilt top and quilting it- it makes no sense to ruin it with a shoddy technique of finishing. you do not save anything, you only make what was good work look poor. sorry...my 2 cents worth...i have never seen a complete machine stitched binding that did not look like a machine stitched binding.