I did not have to interview with my peers, but this is my fifth year teaching, my first at a Catholic School. Some of the things I was asked in my interview (with my principal and AP) were about discipline, comfort level with teaching religion, and why I was looking for a job in Catholic Schools.
With discipline, the importance is consistency and structure- ESPECIALLY in middle school. I love my Catholic School, but was a bit unrealistic about what the job would be like. I assumed it would be exponentially better than public school- and it is, but it is still a school, the kids are still kids, and the parents are still parents. Take that for what you will
Patience is key, and I don’t know if you’re new to teaching, but something I have learned (and most people I work with had to learn too) is that teaching is all about going home for the day, coming back the next morning and starting something all over again, no matter how much extra time/stress/preparation/creativity it takes if it didn’t work. Flexibility, flexibility, flexibility! Good luck!