Normal construction and household debris is fine. The restrictions come from Illinois law and from what the receiving landfill will take.
State law keeps televisions, computer monitors and other listed electronic items out of Illinois landfills, and tires, lead-acid batteries and landscape waste each travel their own route. None of them belongs in a mixed load.
Hazardous waste, liquids, paint, solvents, fuel and asbestos are out as well, as they are everywhere.
Worth knowing: the City's curbside service does not take building materials at all, and it will not take appliances, water heaters or other bulky items either. That is exactly the gap a roll-off fills on a remodel.
Anything you are unsure about, raise it with your account manager before it goes in.