Just to add, I think you might be hard-pressed to find a DrPH/MPH that's only four years total. Do you already know of one?
As Stories indicated, the MPH is a prerequisite; after this, most programs expect work experience (3+ years) in public health. The DrPH program I'm entering is five years, so the time for both degrees (for me) will have been seven years, excluding the time I worked in-between. (Though I am hoping to maybe shave one year off the program by transferring credits from the MPH.)