Ordinary construction and household debris is fine. The limits come from Illinois law and from what the receiving landfill will take.
Illinois treats yard waste as a separate stream, and the rule reaches the person loading the container rather than only the hauler. State law says no one may knowingly mix landscape waste intended for landfill disposal with other municipal waste, or put landscape waste into a container headed for a landfill unless the container itself is biodegradable, and a sanitary landfill may not accept landscape waste for final disposal. So grass, leaves, branches, and shrub cuttings need their own arrangement.
Hazardous material stays out everywhere: paint, solvents, fuel, used oil, pesticides and their containers, pool chemicals, asbestos, and anything radioactive or explosive. Village code puts pesticides, pathological waste, and explosive waste in its own hazardous category.
Tires, batteries, and appliances holding refrigerant are handled separately and should be mentioned when you book rather than loaded quietly.
If an item is borderline, ask your account manager before it goes over the rail. One wrong item can reprice a whole load at the gate.