As with most legal questions, the answer is: sometimes. You can never pass a school bus when you and the bus are going in the same direction, regardless of how many lanes a road has. However, on a 4-lane road with at least 2 lanes of travel going in each direction, you need not stop for a school bus stopped in the opposite lanes of traffic. For example, if you are driving eastbound on a 4- or 5-lane stretch of Roosevelt Road in Wheaton, you need not stop for a westbound school bus.
Illinois imposes serious penalties for improperly passing a stopped school bus, which is probably why drivers can be overly cautious when they see a stopped school bus on a 4-lane road. If you are convicted of improperly passing a school bus, you cannot receive court supervision and the Secretary of State is required to suspend your license. The mandatory suspension period is 3 months on a first conviction, which is a long time to go without a car.