I don't go to those schools so I can't tell you anything about them. I heard that Washington is very competitive but I'm not reallly sure.
The school I am currently attending, Loma Linda University, also has the MIP program (MPH and Peace Corps). MPH programs you can enter are: International Health, Health Education and Promotion, and Environmental Health. I don't think it's hard to get in the MIP Program or the regular MPH track. I really had a great time with International Health MPH at Loma Linda, especially during ICD, the class that we take internationally during the summer. Our destination was in Madagascar and Mauritius and it was such a great learning experience. We met with active NGOs in those two countries plus local villages and their Ministries of Health. Travelling was a plus as well. This class was an introduction to living life in a third world country, and some of my classmates did not like living or working in a developing nation, so at least they got to know that before signing up with a 2+ year involvement with any NGOs or Peace Corps. Loma Linda U also has this program where they provide scholarship to returning Peace Corps volunteers who want to pursue MPH after their service. If you have questions about our programs let me know.