This was a new role at the time and I was not pressed to change jobs so I was willing and able to let the process take its due course. Over the course of a year I was brought in twice (flown to NY both times) and meeting with a total of 14 - 18 people. Some were at the level I applied for, some above (up to the Chief Commercial Office and current CEO Robin Hayes) and some below. They were from all over the organization: People, to Marketing, to Planning, to IT.
Culture is important; they want you to drink the 'blue juice'. They want smart, hard working, talented people who are helpful, likeable, and engaging. They believe in servant leadership. If you will be in management it is primarily how will you serve those who report to you. How will your needs take a back seat to their needs (and this flows up so don't worry, someone is looking out for your needs).
They want people who will move around while in the organization. So while you may be a great Schedule Manager, or Inflight Base Manager, or Advertising Manager, or IT Release manager be prepared to talk about what else you want to do. I was in the Commercial & Planning team but had I stayed Inflight Management would have been my next stop.