Construction and demolition debris is welcome in an Avon container. Ohio allows it at municipal solid waste landfills, so a mixed remodel load is straightforward.
Ohio draws its lines elsewhere, and two of them surprise people. Along with hazardous waste, regulated PCB waste, bulk liquids or anything with free liquids, and untreated infectious waste, the state keeps scrap tires and yard waste out of landfills entirely. The Ohio Environmental Protection Agency sets this out on its own landfill page. Grass, leaves, and brush need to go to a composting route instead.
Asbestos cannot ride in a standard container anywhere in the area, and the county facility refuses it in any form. Paint, solvents, fuel, propane tanks, used oil, and batteries also stay out. Lithium batteries deserve a special mention, because the city warns that the ones in phones, laptops, and tablets can start fires when crushed.
Avon adds a rule of its own that is worth knowing. Waste made, collected, or accumulated outside the city limits may not be brought into Avon for disposal, so a container cannot be filled on a job in another town and dropped here. Ask your account manager before anything unusual goes in.