Education in biomedical and health informatics (BMHI) has been established in many countries throughout the world. For degree programs in BMHI we can distinguish between those that are completely stand-alone or dedicated to the discipline vs. those that are integrated within another program. After running integrated degree medical informatics programs at TU Braunschweig for 10 years at the B.Sc. and for 15 years at the M.Sc level, we (1) report about this educational approach, (2) analyze recommendations on, implementations of, and experiences with degree educational programs in BMHI worldwide, (3) summarize our lessons learned with the integrated approach at TU Braunschweig, and (4) suggest an answer to the question, whether degree programs in biomedical and health informatics should be dedicated or integrated. According to our experience at TU Braunschweig and based on our analysis of publications, there is a clear dominance of dedicated degree programs in BMHI. The specialization in medical informatics within a computer science program, as offered at TU Braunschweig, may be a good way of implementing an integrated, informatics-based approach to medical informatics, in particular if a dual degree option can be chosen. The option of curricula leading to double degrees, i.e. in this case to two separate degrees in computer science and in medical informatics might, however, be a better solution.