Underlayment height for tile / carpet....
When properly fastened, 3/4" plywood subfloor with joists at 16" o.c. and joists not overspanned, should give you a good subfloor. Adding another layer of plywood of course is always a good idea, the more the better. You should be fine with 1/2" underlayment. You decide the levels you want and whether to go thicker in the carpeted areas.
Rather than 1/2" backer board under the tiles, you can use 1/4" or even better Ditra membrane which adds only 1/8".
Subfloor is 3/4" t&g exposure 1, nailed and glued to the joists. Underlayment is square edge B/C grade spaced 1/8" and fastened only to the subfloor, not the joists, no glue for the underlayment.
Let me know the type, size, spacing, species, grade and unsupported span of the joists. We always start with the framing.
Tile 4 You LLC Troy, MI
KERDI Shower Specialist ... DITRA Installs ... Product-Method suitability consultation. I have NEVER made a mistake, I thought I did once...........but I was wrong! - PRODUCTS ADVERTISED WITHIN MY POST ARE NOT ENDORSED BY ME!