Ordinary construction and cleanout debris loads without trouble. Lumber, drywall, siding, shingles, flooring, tile, cabinets, doors, windows, furniture, carpet and cardboard are all fine, and clean brick, mortar and concrete belong in the smallest unit.
The hazardous list stays out, and the reason is the receiving site rather than a town rule: paint, stains, solvents, thinners, fuel, motor oil, antifreeze, propane cylinders, pool chemicals, pesticides, asbestos-containing material, wet batteries and liquids of any kind cannot be buried and cannot travel in a container.
Tires come out as well. They need a separate route, and leaving them in usually means the load is repriced or refused.
Appliances holding refrigerant, so refrigerators, freezers, water coolers and air conditioning units, need the gas recovered by a certified technician first. On a Morrisville townhouse that often means the heat pump or air handler is a separate job from the container.
One local point is about origin rather than material. Because Wake County's landfill takes no waste generated outside the county, a load mixing debris from a Wake County address with debris from a Durham County address is a problem rather than a saving. On a project spanning the line, keep the loads separate and tell your account manager which address each one came from.
If an item is borderline, say a part-used tin of stain, a sealed drum or an old television, run it past your account manager before it goes in.