An interview is certainly not a guarantee for admission. I commonly see 30-50% quoted as "acceptance rates". However, there is nothing wrong with a December interview... nor is it really that late. Of course this depends on many things (i.e., when you submitted, your stats, the schools, etc.). Your stats don't matter all that much one you get an interview -- at that point, you just need to own the interview. There's really nothing else you can do, right? They wouldn't have invited you if they didn't think you could be a good fit for the school.
I think it is far more likely that you will get interviews at more schools... so it's premature to freak out about the one you currently have an interview at. Don't waste a single minute thinking about what your friends have accomplished. I have friends at HMS, Michigan, JHU, etc... there will always be people who are apparently more successful. Just speaking from my experiences. 🙂
Good luck!