Ordinary construction and cleanout debris is fine: lumber, drywall, roofing, siding, flooring, cabinets, doors, furniture and household junk.
Hazardous material is not. Paint, solvents, fuel, motor oil, pesticides, farm chemicals, antifreeze and batteries all need their own route. The regional district advises that leftover paint be dried out with sawdust or cat litter before it goes anywhere near regular trash.
Tires stay out of the container. The regional district runs tire collection points for exactly this reason, and a tire found in a load can hold up the whole delivery.
Electronics come out too, and most large appliances are handled separately rather than recycled with a mixed load.
Asbestos never belongs in a standard container. Older Delta farmhouses and outbuildings can hide it in siding, floor tile and pipe wrap, so if you turn some up mid-demolition, stop and call your account manager before anything else goes in.
The receiving facility posts what it will and will not take at its access points, and that posted list governs on the day. Your account manager checks the current list with the site before your load is booked.