I don't think there is anything double-sided that would fuse such thick materials together (unless they can both take a lot of heat and pressure; you could test on some scraps to find out). What I would suggest is pressing a lightweight interfacing, as imsewnso suggests, on the wrong side of each fabric first. Then spray baste or glue baste the two pieces together. I would cut the interfacing to the correct pattern size before applying.
If you go to Walmart or JoAnn's, look for interfacing that says "lightweight" or "featherweight" or "sheerweight" and fusible. Pellon has several of these. Here is a link to one on Amazon, but there are others too:
http://www.amazon.com/gp/product/B00...=sr_1_1&sr=8-1
At Walmart and JoAnn's, you can get just the yardage you need cut off the bolt.