Avid Media Composer 8 - is it possible to edit two video sessions at same time?
Are you talking about having two projects open at one time? As far as I'm aware, Avid MC doesn't let you do that. 

But you can import Bins from another project and technically do what you want that way. Otherwise I would just make one project for all the interviews, and separate them with bins if they're all sharing some elements.

EXP:
Interview1 Bin (containing the clips for interview 1)
Interview2 Bin (containing the clips for interview 2)
SFX (Shared sound effects) 
Music (Shared music) 
GRX  (Shared graphics)