I press my binding three times. First, press in half before sewing. Next, after sewing warm the seam and then press the binding toward the edge. Last, fold the binding over the edge and press again from the back side.
I cut the binding two inches wide and can still stitch-in-the-ditch from the front side and catch the binding on the back if so desired. I usually finish the binding by hand stitching, but I stitch-in-the-ditch from the front side for charity quilts.