We just bought and I just started renovating an old (c. 1910) house that was completely renovated in 1974 or so. It's our third house of similar vintage, so I have had some practice.

The closets still have (mostly) original horsehair plaster on lath walls, but the rooms have been refinished in a product I've never seen before. From the stud side, it looks like approx. 5/16 inch gypsum wallboard with a paper backing, but then in the middle there's another 5/16 inch layer of what looks like cement, then a very smooth 1/8 inch finish layer. It's crazy heavy, as you would expect, and rock-hard. It's also in great shape as it has been covered with wallpaper for decades, possibly since it went up.

So is this 1974-vintage cement board? And a couple of follow-up questions:
It sanded and took plaster and paint very well in the first room I did, but I want to tile the bathroom and don't know if I should just scour and clean the surface or put up a backerboard. Cement backerboard on cement board sounds like overkill overkill?

And finally, when I stripped (about 4 layers) of wallpaper before painting the first room, the final layer was a navy blue/black-and-tan vertical stripe on paper so thin I can't imagine it was hung after it left the factory. I don't know if this was for easier install or if somebody was selling pre-finished cement board in 1974. Any suggestions or cautionary notes would be most appreciated.
Thanks!