Well... for video editing (until now) I mostly use Vegas (and still researching because I started with this about 2 months ago).
If I do music audio mixing (megamix) I do it separately with Adobe Audition, Soundforge, Decadance and some VST plugins.

About Your question, I do not know which part of the video are You reffering to but it is mostly done with masking 2 clips in the same time period. Put one above the other, adjust them to fit the screen as You like and mask both to get 2 squares.