I can't remember the "mil" on them but I used heavy duty yard bags to line my wooden molds. It's been several years and I still have them. My husband made my molds and one is not exactly like the other so I cut the liners specifically for each mold, just like it shows in the video.
The great thing is I don't have to throw the liners away, I can reuse them to my heart's content. My molds have lids so I also cut a strip to cover the top of the soap before I put the lid on. When you are ready, you just lift the liner out, soap and all. The liners can get a little oily after time but since you can make several out of one trash bag, it's not at all expensive.