Waterproof membrane in bathroom?

Hi, late last year I bought a 1950's semi which i'm currently renovating entirely myself. The most recent room to undergo renovation is the bathroom... on first floor, traditional wooden joists with 15mm floorboards on top, used to have a bath in it but am turning it into a shower room... i've near enough completed the floor-ceiling tiling on all walls and hope to tackle the floor this weeked.

The tiles i'm using, floor & wall, are 60x40cm honed/filled travertine... for the floor these will sit on top of hardibacker board... tiles will of course be sealed but as an extra level of protection to the floor below is it worthwhile to put a waterproof membrane down? Something that sits between the current floorboards and the hardibacker?

First time tiler... not sure if i'm overcomplicating things?

when you say...shower room..??

is this a wetroom with a former ..or...

a shower room with a tray...?

Trust me to leave out the vital bit of info... shower room with a tray... low profile, mounted/glued directly onto the original floorboards... not ideal I know.

you will be ok with the hardie boards staggered and glued and screwed.

and there is no deflection in the floorboards what so ever.

Cheers, i've screwed & glued down the hardie boards, also gone round with sealant and sealed all the joins between boards.

Deflection of the floorboards... do you mean movement of the floorboards underfoot, like bouncing/flexing when you walk on them? Or boards that have deflected and become misshapen or a little warped?

There is no floor movement underfoot, least nothing noticeable, the spacing between joists is 400mm and the joists themselves are 63x220... some of the floorboards are a little misshapen, for the most part still flat but one or two have a slight U shape to them. The floor as a whole though, and over a length of 1.56m slopes down by about 4-5mm

you should be alright with that.the 4-5mm you can make this up with adhesive,by back butter the tile a little heavier.