My experience removing double-sided fusible interfacing is not good. The single-sided fusible can sometimes be removed by holding the steam iron above it for 10-15 seconde to loosen the glue and then gently pull off the stable backing - however sometimes you are left with sticky. With the double sided fusible, the only thing I have found that works is to cover it with a very thin cotton batiste fabric (and yes, I did try chiffon but it was not pretty). The pieces will be slightly thicker but they shouldn't be too stiff.
When ironing the pieces that have the double-sided fusible, I use a piece of waxed paper next to the iron - and another one on the ironing board. I have also used freezer paper with the shiny side against the sticky, but I prefer waxed paper.