There are lots of interpretations of this character because Edgar Allan Po does not like to simplify things. Madeline can be not even a real human. The evidence proves that the narrator does not see her all the time, and they do not interact with each other. An author could use this character to show two sides of Roderick’s soul, Madeline being his greatest fears. That idea explains her unexpected appearance after the death. Another viewpoint state that this character is just a supernatural creature which exists in the house full of mystery and secrets.
Madeline Usher in the Essays