Ceiling tile replacement with drywall

Hi everyone,
Im replacing the ceiling tiles in my home with drywall. There are 2 kinds of ceiling tiles in my home.In one room they are 12 by 12 ceiling tiles glued to what seems to be plywood( I removed one of the ceiling tiles to check) . And above the plywood there are the rafters with roll insulation in between them .The rest of the house has 9 by 9 ceiling tiles stapled/ nailed /glued ? to furring strips .(I can see furring strips at one of the edges where the ceiling meets the wall thats how i know its different from the other room, although im not sure if its glued/stapled or nailed).The ceiling tiles tested positive for asbestos so i will have it professionally removed and then do the drywall myself . My main concern is if I go this route will I be loosing some insulation ? because from what i understand ceiling tiles are much better insulators then drywall. If so do i add some type of insulation between the plywood and the drywall?also will the drywall go directly under the plywood ceiling or is there anything else that i need to put in between (some type of underlayment or moisture barrier etc? ). OR should i put up drywall on under the ceiling tile and not bother removing them ? Any help would be appreciated.
Thanks
Sean

 

Ceiling tile r value is pretty minimal, so I wouldn't worry too much about that. Problem with going over the ceiling tile is you can't see where your Nailers are for sure which presents a problem for hanging. There is strapping above the ceiling tiles which you might be able to reuse if it is secure and spaced evenly. You want drywall hung perpendicular to the strapping. Or if you decide to take the strapping off, hang it perpendicular to the joists. Main thing to look for is that the rim joist on any exterior wall is well insulated so that your don't have wind blowing above the ceiling.
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Thanks! For the room where i thought it was plywood Upon removing the ceiling tile the ceiling above it was actually drywall with wallpaper. Wall paper that looked like wood . Any ways i was able to use a stud finder to find the ceiling joists. I installed drywall anyways in order to encapsulate any residue of asbestosand i figured its an extra layer of insulation and painting it is much easier then the old drywall with glue stains.