The only reason his family members had to go through security in AZ was because they were coming from Mexico. When you have a connecting flight and you're on an international flight, you have to go through security + recheck your lugggage. If it's just a regular flight within the US, there should be no reason for you to have to go through security a second time.

When I used to fly (but I had a valid ID, not a foreign passport), I never had any problems on layovers. Then again, all my connecting flights were either Dallas/Ft Worth, Chicago, and once Denver. It's always a risk to fly when you're undocumented, but I wouldn't worry too much about the connecting flight.

Good luck!!