Also, you can get your MPH if you do a preventive medicine residency. Some places offer a combined residency (such as medicine/preventive medicine, etc). Dartmouth offers just about ANY combination with PM (even path, rads, ortho!).
PM residencies are typically 3 years (one academic, one "clinical" - aka, intern year; and one doing a practicum). If you do a combined program, your intern year is taken care of. During your academic year, you earn your MPH.