Before you join the pieces in the center, make sure that your seams are "spiraled" when they meet. Depending on the type of paper you are using (i.e. regular photo copy paper, or thinner paper) It may be easier to tear away the paper ONLY from the seam edge of the two pieces - but it will make it more difficult to match the seams.
also ... I usually baste my pieces when I join them, flip them open to make sure the seams match, then I sew over the basting stitch with a smaller stitch.