Berkeley engineering does require upper division H/SS breadth: http://engineering.berkeley.edu/student-services/degree-requirements/humanities-and-social-sciences .
South Dakota Mines requires engineering majors to complete at least one advanced H/SS course: http://ecatalog.sdsmt.edu/content.php?catoid=8&navoid=1334#General_Requirements
I do not know of any California public that requires upper division math or science courses for H/SS majors. Which ones were you thinking of?