He miss his parents,------work far away from his hometown.

如果填both of them的话,前面是一个句子,后面又是一个句子.
而中间没有,and 之类的连接词是不合语法的.
当填both of whom时,是非限制性定语从句,完全ok.
both of whom将前后两个句子连接起来,构成一个完整的长句.