We've had some luck recycling ceiling tiles and carpeting, but haven't yet been able to manage the C&D waste. Armstrong has a ceiling tile recycling program that's pretty simple and straightforward. You can find details on their website. You'll need to locate a local Armstrong products distributor who also serves as the ceiling tile recycler (not all Armstrong dealers do), follow the guidlines, have a clean place to stack the used tiles, shrink-wrap them, and work out a way to transport the stacks to the distributor. It's a bit tedious, but Armstrong has been doing this over ten years now.
Carpet can be recycled in a similar way. All of the major commercial carpet manufacturers (Shaw, Mohawk, et. al.) will recycle used/old carpet, mostly poly-propylene #6 fiber. If you go to Shaw flooring website and search around their sustainability info, you can link to a national network of carpet recyclers where you can find one in your area. Or, speak to the sales reps.
C&D material is supposed to be low-hanging fruit, but with commercial construction material it's not so easy. Most commercial construction wood is engineered laminate, which contain glues and resins, and therefore isn't suitable to be ground into mulch. Drywall is problematic unless you live in an area where it can be used as compost or soil amendment, but again, that needs to be stage separately and kept clean. Metal studs can be recycled, obviously.
A big hurdle with C&D recycling is lack of space to separate and stage the stuff before sending it along. Here, a local green landfill that takes C&D debris wants it separated (aggregates, metal, wood, drywall, etc.), but we don't have the space or the dumpsters to do that yet. We could (and do, sometimes) divert wood scrap from our carpenter shop to the College of Art or a local school, even to Surplus where it's sold at auction. Again, it's mostly plywood scrap that can't be used for compost. Mixed drywall and non-hardwood wood product that could go to the green landfill can only be ground and used as daily cover for the local trash landfill, which, though a positive, isn't exactly recycling it. And, again, we don't have the space for separate dumpsters to collect C&D debris.