For a 100A subpanel, I recall running 2-2-2-4 aluminum SER. That was for a short run though, you may need to upsise if your run is long enough to cause more then the allowed voltage drop at full ampacity.
2-2-2-4 AL SER is perfectly fine for... [ahem] "120/240-volt 3-wire, single-phase service-entrance conductors, service lateral conductors, and feeder conductors that supply the total load to a dwelling unit and installed in raceway or cable with or without an equipment grounding conductor. The grounded conductor shall be permitted to be not more than 2 AWG sizes smaller than the ungrounded conductors..."
The point of contention is the "total load to a dwelling unit" part. 1-1-1-3 AL can handle 100A without any qualifiers. He should be able to get away with 2-2-2-4, but that's at the discretion of the inspector.
(I used 4-4-4 aluminum "Periwinkle" triplex cable, overhead to my
detached garage for a 60A feeder, then transitioned to two #6 copper and one #8 from the weather-head to the subpanel. That was code at the time but would be illegal today.)
If you really want to see something scary, look up the cost of 3-3-3-5 copper cable.