Rookie;
I did classes for my MPA degree in my last two years of medical school. DMU (formerly UOMHS) offers dual degrees in health care administration and (this year) public health along with medical degree.
The class load wasn't too over burdensome.
Classes are offered evenings and weekends. Two of my classes were self-study (probably the most time-consuming). If you want to get an additional degree and they are offered at the medical school you are attending, I'd do it there. DMU schedules the dual degree classes so they fit well with the requirements of the medical students. Plus, there is a tuition break for medical students for the Master's courses.