Not Spanglish; just a typo for "terna": a very common one with scanned documents; "rn" is very commonly OCRd as "m", and "tema" is a much more common word than "terna", so it's understandable.

If you look for "la tema examinadora" in Honduras you'll find quite a few examples, but more of "la terna examinadora", which is what it should be.

"Terna" means a group of three. This number is widely used in Spain too, at graduate level. But in practice I don't think you need to include the "three-member" part. Just panel or committee, whichever you think more suitable (committee is more common in the U.S., I think).