Hi shorteared!
I tiled my bathroom floor using something similar. It has a sticky side that looks like tar and it's used as a underlayment. It's made out of styrofoam, easy to cut and no tape needed if your using flexible mortar. You apply the mortar right to the mat. I believe it's called easy mat

but anyway. It's water proof and sound proof. The only way I know someone's in the bathroom, I hear the exhaust fan or the shower

love it! I was told if I ever want to replace the tile, it will be less of a hassle. My house is on a slab, so when I do the tile in the kitchen, it will be my choice.
Are you going to tile the basement floor?