Is this a common honors-designation system? At my undergraduate university, one could earn three types of honors that are designated on your diploma:


Departmental Honors, where the requirements are set by the department, usually involving a thesis.
Interdisciplinary Honors, which involved an interdisciplinary curriculum of about 45 credits (nine classes). In my opinion, it was a valuable program.
College Honors, which is what you get when you do both.


I earned College Honors, for both doing a bachelor's thesis and completing the interdisciplinary requirements. 

Would graduate schools know what it means if I put "with College Honors" on my resume/application? I assume not, but Latin honors seem to be common enough. Is it worth explaining? Or should I just designate them both and not even bother with the "College Honors" phrasing?
The "College Honors" is definitely not a common distinction. I would also list the Departmental Honors, which is certainly something that is frequently encountered, as well as the Interdisciplinary Honors. You're truthfully representing your credentials, and it will be easier to understand.