Both Jim and Jean are teacher.

有问题，teacher --- teachers
两个人，是复数。

没 有

both 表示两着都… 可以表示副词,也可以做代词,例:
副词:We are both students.
代词:Both of us are students.

这句话中both明显是代词，指代Jim和Jean，所以应该用students

teacher -> teachers