not only my father but also my mother is a teacher.还是not only my father but also my mother are teachers?

not only my father but also my mother is a teacher.是正确的.
not only.but also这个短语采用“就近原则”,即谓语动词用单数还是复数,取决于离谓语动词最近的名词.这个句子中,离be动词（is）最近的是my mother, 为单数,所以be选择用is.
例如：not only you but also his parents like swimming. (离谓语动词like最近的是his parents, 谓语动词用单数形式like,而不用加s)

both意思为“两者都是”,即主语为复数,则谓语动词要用复数形式.
both my father and mother are teachers.