Most renovation debris is fine: lumber, drywall, plaster, roofing, flooring, siding, cabinets, fixtures, furniture and general cleanout material.
Hazardous and liquid material stays out in every case. Paint, solvents, fuel, used oil, pesticides and asbestos all need their own route, and so does anything holding refrigerant. Appliances with refrigerant gases are only handled once those gases have been properly evacuated.
Indiana adds a rule that catches landscaping work. Vegetative material may not go to a solid waste landfill except for grass, and for woody material under three feet long that is bagged, bundled or otherwise contained. Sod, dirt, rock and sand are not treated as yard waste at all, so a landscaping job usually needs its own container rather than a share of the renovation one.
Electronics, tires and car batteries are the items that most often spoil a load. The Lake County Solid Waste Management District runs household hazardous waste events, computer and television recycling, tire recycling and latex paint recycling for exactly these, so they have somewhere to go that is not your container.
Burning is not an alternative: the Town makes it an offense to openly burn or ignite refuse or garbage of any kind.
Ask your account manager about anything borderline before it goes in, because one rejected load costs more than handling the item separately.