Complex sentence: A combined internal medicine and psychiatry residency program is a post-graduate medical education program in the United States, which leads to board eligibility in both internal medicine and psychiatry i.e. a graduate of the residency is both an internist as well as a psychiatrist.
Split into simpler sentences: A combined internal medicine and psychiatry residency program is a post-graduate medical education program in the United States, which leads to board eligibility in both internal medicine and psychiatry. That is, a graduate of the residency is both an internist as well as a psychiatrist.