I only know about MD/MBA and MD/MPP programs, but most schools encourage you to apply to their MBA/MPP programs after you have been admitted to their medical school. Harvard and Dartmouth are notable exceptions for the MBA that accept joint applications, but HBS will let you apply in your first year at HMS (not sure if the same is true for Tuck/DMS). In most cases, as far as the medical school is concerned, you're just another MD applicant, but they do sometimes let you note that you are interested in joint programs on the AMCAS or secondary application. The only difference I can see it making is if you can make a case that you will actually put that joint degree to good use by demonstrating a strong interest in the overlap of medicine and the other field.
