Another interesting, yet morbid and controversial, twist to the twins link is that the Usher family most likely has a history of incest, which means their family has been "inbred" for centuries. Incest can lead to offspring born with mental illnesses, along with other maladies, so this ties into the twins story well.
Richard and Madeline are a lot like the two halves of the yin-yang: both light and darkness paired in balance with each other. Because they were twins, there was a closer biological and symbolic bond between the two. Just as the house is separating but singular, twins are the same way, reproductively speaking.
A single egg splits, and two entities are formed, much like the splitting or cracking of the Usher house. The metaphor is extended by Poe's choice to make the two characters twins. If they were only brother and sister, the symbolism would not have been as complete.
For a closer identification. To be a twin is to be identical (ideally), and twins share more than other siblings. They share the same womb environment, and, due to being the same age, move through life at the same stages, experiencing the same history. Culturally, there is the association that they share some closer mental or spiritual link. (Think of the movie "Twins" for an example.) This link fits with the sense that they are the same person, or interwoven at a greater than physical level.