Parallelism from a grammatical or syntactical perspective can have various meanings. A writer can demonstrate parallelism if he uses the same word order (subject, verb, direct object) in phrases or sentences closer together. Similarly, a writer might use parallelism by choosing words with the same ending for a series within a sentence.
A good guide for initially perceiving if a sentence is parallel is to read it out loud so that you can hear if it flows well. If you stumble through the sentence and have difficulty deciphering the author's meaning, chances are the sentence is not parallel.
Keeping the above elements in mind, look at the sentence you have supplied as an example.
Mrs. Manybears was not only a patient woman, but also understanding and sympathetic.
The sentence contains several problems with parallelism.
1. Notice the words in bold. They are acting as adjectives in the sentence, but instead of the author eliminating wordiness by placing the adjectives in a series before the wordwoman, she carries two of the adjectives over into an unnecessary phrase. See how the sentence flows better when it is parallel.
Mrs. Manybears was a patient, understanding, and sympathetic woman.
2. If the author of your sample sentence would like to emphasize Mrs. Manybears' patience, she can still do so with parallel structure. Below is the second revision of the sentence focusing on balancing phrases/clauses by using about the same number of words and the same word order.
Mrs. Manybears was not only a patient woman; she was also an understanding and sympathetic individual.
While this revision is wordier than the first revision, it still demonstrates parallelism. See how the word order is essentially subject, verb, adjective, predicate nominative in both clauses?