Yep. My first wooden mold batch, I used regular butcher paper (the unlined kind) and the oils leeched through the paper and I had a hard time getting the soap out of the mold. I had to take the ends off then push on one end with the heel of my hand until it finally popped out. Speaking of which, I need to pull out the mold and wash off the baking soda to see how the smell has been absorbed/dissipated.
Reynolds Freezer Paper is plastic lined on one side and it would have been perfect if I hadn't poured at such a light trace that it leaked through the folds where I forgot to tape them closed

But otherwise, it was great - pulled right out of the mold and right off the soap. Just make sure the plastic lining goes on the soap side.