Bibliotherapy is a way for readers to heal by reading about characters and stories similar to their own.
"...Ideally, the process occurs in three phases: personal identification of the reader with a particular character in the recommended work, resulting in psychological catharsis, which leads to rational insight concerning the relevance of the solution suggested in the text to the reader's own experience. Assistance of a trained psychotherapist is advised." --bibliotherapy in ODLIS, Online Dictionary for Library and Information Science.
Books in this list include characters dealing with various types of mental illness.