I was hired about 4 years ago so I don't remember everything. I believe that we took the drug test at the time of the interview as well but didn't start the background check until we were selected and offered a position with the company. The background check can take any where from 2 weeks to a month depending on how many jobs or moving you did. They have to trace you through the past 10 years and will want you to account for everything. Mine took longer because I had to find a way to verify employment with a previous airline that went out of business.
What city did you interview in, if I may ask.