I'm not quite sure what you're asking, but I have an inkling, so here goes: The "upper world" and "lower world," in the world of the play could be better expressed as plot and subplot.
There are often, in Shakespeare's comedies, high born characters that populate the central plot of the play -- in this case, Isabella, Angelo, and to some degree the Duke -- and lower born characters that populate the subplot of the play. The subplot often mirrors the main plot, giving a sort of commentary on the plot.
The main plot of this play revolves around a woman, Isabella, who has pledged to become a nun pleading for her brother's life (mercy) to the Deputy that is in charge in the Duke's absence, Angelo. Angelo agrees to release her brother in exchange for a sexual tryst with Isabella.
The simplest illumination provided of this plot by the subplot characters, is that the subplot characters are corrupt, licentious people living outside the laws of "decent" society. These characters could be said to demonstrate Angelo's real demeanor, and the sort of life he would act out behind closed doors. The subplot characters, however, do so out in the open.