Yes. The sentence with correct parallel structure would be as follows. The doctor known only that her patient would improve, but also knew that her patient would [can't understand the sentence after that, but nevertheless it is still faulty].
The answer is yes. However, the other respondent provided you with an inaccurate (and non-parallel) sentence correction. The correct syntax -- and parallel structure -- is... The doctor not only knew that her patient would improve, but she also knew that he would completely recover.
