Ohh thanks j-weezy and seraph! Ok, so if the OP doesn't know, I have been summoned because I am applying for a history of medicine MD/PhD this cycle and come from a heavy science background. You can see my MDApps for all the details. So, you can do a humanities/public policy focused MD/PhD. That being said you need to seriously think about this path. Disclaimer: I am not a pessimist about this, just a realist. This is the same advice I got last year and feel it's my duty to pass it along since you asked.
So here we go...
1. There are a select number of programs that will even let you do this type of program. Personally, I found 13 of them. For public policy or ethics the list is likely similar but not identical so you need to start calling every medical school you are remotely interested in and ask. Call the MD/PhD office at each school and ask if they will look at your app and if so do they have anyone else doing humanities PhDs and what are their admissions policies for these people (GRE, separate app to PhD, funding levels). Be prepared for hostile responses from some places.
2. Without coursework and research in the field you want to do your PhD in you are going to have a difficult time convincing both the PhD people and the MSTP that you know what you're getting yourself into and why you want to go the non-traditional route. If you are serious about this I would highly recommend talking to professors at your school, getting yourself into relevant classes and starting research. Take an extra year in college or a year off if you have to. This is no different than applying MD/PhD in the sciences - you must have the research qualifications. There is only one person I know who came from a science-only background who is now doing a humanities MD/PhD. However, she was accepted to do MD/PhD in the sciences and later changed her mind and went into history of science. Luckily she is at Penn and they support these students already.
This is a very important point because several programs (UChicago, Harvard, Michigan, and Penn (unofficially)) make you apply directly to the PhD program and you are considered as though you were a PhD-only student by that department. This proved difficult for me because I do not have a history major in undergrad nor a masters degree, which many people applying to history PhD programs have.
3. Even with everything you are supposed to have to be a competitive (research, GPA, MCAT, appropriate LORs, volunteering, etc) you are at a disadvantage because you are different. You have to be at peace with that. Bottom line is MSTP is created for people who want to do lab sciences so you have to might your way in. You can't give them a reason to say no, because they're likely looking for one.
4. I can't stress enough the value of making contacts at the places you are applying. You need someone there to advocate for you. Also try to find practicing MD/PhDs in your intended area to give you advice and help you make those contacts.
5. Be ABSOLUTELY sure this is the path you want to take. Think it over very hard because this is not an easy path. You will find people out there to support you though and with a lot of hard work it is possible to get a spot.
Ok, I hope I haven't been too discouraging. People on this board can attest to the fact that this year has been an emotional rollercoaster for me. I am very happy to have an acceptance and a couple more likely coming. That being said, as a science applicant I know I would have had many more options. Ultimately this is a big risk and it takes a lot of courage I think to take this path. But, you only get one chance to do this type of training and if your heart is in the non-trad path then go for it! Feel free to ask me any other questions that come to mind. I really hope this has been helpful.