What is the proper term for when characters in a novel have similar, or "parallel" situations or traits? For example, Frankenstein and his Creature.

I think what you're talking about is a "foil" character. 
Foil characters need to have some significant things in common, but they differ in at
least one important way.  For example the characters may both be the same age, gender,
class, etc but when presented with an important decision, one character chooses the
"right" path and the other character chooses to do wrong.  Or perhaps an author has two
characters that are similar in some important ways and even act the same when presented
with a certain conflict, but one character is male and the other female.  The author
then may be examining how the same situation affects characters of different genders by
using foil characters.

Most often one of the characters is
the novel's protagonist and the other a minor character.  The minor character (as a
foil) is present to highlight some major characteristic of the
protagonist.

In the case of Frankenstein, perhaps the
creature and creator are both outsiders but how they react to a public that dismisses
and marginalizes them is different.  This could be the author's way of highlighting the
different reactions of society to modernity/science/technology/ or the
"other."