G.B.
Go to Hobby Lobby and get a spool of narrow heat and bond. Then using the low setting on your iron you bond them together. Heat and Bond, the one that is least heavy duty, melts and bonds the fabrics together. It should not show if you get the edge of the strip even with the edge of the ribbon on top.
You can test it on some small pieces for sure. If it shows white underneath then perhaps you're trying to do something that can't be done. Try sewing along the edge of the sheer in a long baste stitch using the same color thread.