My student's middle school math is an integrated courses of "Algebra 1 and geometry" and "Algebra 2 and geometry". His high school accepted both courses for a total of 2 credits (2 yrs). Will this satisfy the geometry requirement for UC?

Yes, as long as his high school accepts it then UC will accept it. This question is addressed on the UC’s website:

‘UC-approved high school courses Three years of college-preparatory mathematics that include the topics covered in elementary and advanced algebra and two- and three-dimensional geometry. A geometry course or an integrated math course with a sufficient amount of geometry content must be completed. Approved integrated math courses may be used to fulfill part or all of this requirement, as may math courses taken in the seventh and eighth grades if the high school accepts them as equivalent to its own courses.’ http://admission.universityofcalifornia.edu/freshman/requirements/a-g-requirements/index.html