You can absolutely use parchment paper. In fact, that's what I prefer. (Just make sure it's parchment and NOT wax paper.)
Some people will recommend you purchase special sheets available at stores, they're made of Teflon.
Thank you, Peckish! I have a pressing sheet and I have to scrub it every time I use it because of the residue that sticks to the sheet and it's even worse if you hurry and put the used side down to press the applique! I keep parchment paper on hand for cookies so I'm good to go!!
When you sleep under a quilt, you sleep under a blanket of love.