Sorry if any of this is redundant from what MPHandPscyh said but from 4 epi PhD interviews (2 in person, 1 formal phone, 1 very quick informal phone), there are 2 main things that people seemed to be looking for:
1) Why do you want to go to their program over others? They want to know that you're applying to them because you think they're a good fit and not just applying to apply. You should know why you applied to their program over others: what you like about their curriculum, and specific faculty members' research attracted you to the school. My one informal phone "interview" was solely to assess whether or not I was serious about their program.
2) Why do you want to get a PhD, and where do you see your career going after a PhD? Some people, who are unsure of what the next step is, apply for PhD because its a higher degree, which they think means higher pay and more prestige. But a PHD, is not just the next step after an MPH. An MPH is actually a terminal degree, unless you want to go into research- in which case you will need a PhD. I think there are some applicants who don't realize that the PhD is all about publish research papers. (This is why I think a lot of schools tell students to get a masters first, so they really know what they're getting into). I think you should demonstrate that you've thought about where you see yourself career-wise in 10 years and why you need a PhD to get there. Have a good idea if you want to go into academia, vs. government research. Also, know what your research interests are. You don't have to know what your dissertation topic is now, but I would know what areas you are interested in doing research in (i,e, infectious disease, cancer, environmental epi, etc...) and be able to name a few very specific populations/questions/methods that you want to conduct research in within those fields.
And as a general rule for interviews, be able to explain any gaps or red flags on your resume. You don't need to be perfect, you just need to seem like everything you did was for a good reason.
Good luck!