sounds like you're talking about a single thickness binding ..if so, and want to stitch both sides at once...well, I wouldn't, because I'd never catch them both in one row of stitches. I'd press under one side by one quarter inch, then stitch the unpressed side to the front. Once it's sewn on I'd turn the fabric around the edge of the quilt and pin then stitch the back side in place. Many folks sew it by hand and many sew it by machine....your choice.
In my experience, a double thickness binding will last longer, in case you're putting it on a quilt that will get used a lot. The fabric strip is cut wider, pressed in half lengthwise, raw edges stitched onto front, folded around edge then stitched onto the back.
More details on either process if you need them from many folks on the board.