Hardwood floors + Cement board underlayment?

I'm planning a bathroom renovation in a 1906 house and want to replace a 1950s-era vinyl with an old-fashioned ceramic hex tile floor. All was going well until I thought to pull up part of the vinyl floor to see what was underneath, and discovered that the 50s install was just laid on top of the lovely hardwood flooring that graces the rest of the house. This presents some issues with respect to the tile install I'm planning.

What's there now is, bottom to top, diagonal plank subfloor, hardwood floor nailed to that, some sort of fiberboard (1/4") stapled to the hardwood, and plastic tile glued to the fiberboard. The fiberboard and vinyl will be very easy to remove, leaving a hardwood floor, still apparently with finish on. All I've read about tile installs has said to thinset a cement board underlayment to the plywood subfloor, then thinset the tiles to that. My worry is that the finished hardwood floor won't present the sort of surface needed by the thinset under the cement board. I've read enough on this forum to know that skipping the thinset under the cement board is not a good idea, but the discussions all assumed plywood decking underneath. Should there be some sort of membrane I lay on top of the hardwood before I lay the first thinset?

A side issue is that if _possible_ I'd like to do this without permanently destroying the hardwood, now that I know it's there—if a *little* extra work or money lets me save this happy surprise for some distant future owner of the house, that's great! That said, I plan this tile floor to be permanent and I won't shed tears over the loss of the hardwood that I didn't know was there before and won't be seeing again.

(Also possibly relevant: I haven't ordered the cement board or thinset yet, or for that matter the tile, so if I should be rethinking those, that's an option.)

You need to pull out that hardwood. Then you can go over your plank subfloor with plywood, then cbu thinsetted and screwed down. I do prefer membranes with little mosaics to cbu. Not only does it allow for thicker plywood to be used (the minimum would be 1/2" bc ply prior to cbu), I hate riding over the cbu and backer tape with anything other than square mosaics since the trowel is so small. Noble CIS or Kerdi.