Had a similiar situation with my brother and sister and some friends. To the best of my knowledge, you would have been considered an American citizen up until the time you were 18, given that your father was still in the military and you were his dependent. As you know, the base is considered to be American soil. However, as your mother was German, when you turn 18, you are given a choice of nationality.
Had your German mother divorced him and remained in Germany with you, that might have been a whole different story. I think you would have to check the German laws about nationality and see whether they will grant you dual nationality and a passport on the basis of your mother/grandparents being German. They might have special considerations for American service families?