If you want MD/PhD I would apply at the same time since most schools will only consider applicants applying to both programs simultaneously. It is true and most places will consider you for the MD program separately from the PhD program. If you want to do another dual degree program, I would just go straight for the MD and deal with the dual degree after getting admitted unless you have an endless list of GOOD reasons for getting that second degree. In my experience, if you are applying for a dual degree, the interviewers want to know why you want that second degree. If you don't have solid reasons and some good ECs to back yourself up, you may be weakening yourself in the eyes of the interviewer. I think that in general, if you can get into the MD program, you're not going to have a huge problem getting into an associated MA/MPH/MBA program since they tend to be less competitive than MD. That being said, there is no guarantee that you'll be accepted into an associated degree program once you've matriculated to said MD program. If having that dual degree is an absolute MUST, then you have no choice than to apply to the dual programs since getting accepted simulatenously for both degrees is the only way you can be sure that you're going to get both degrees.
I'm pretty much in a similar situation. I've applied to several MD/MBA programs but for the more competitive schools, I stuck with just the MD so that my interviews don't become a liability.
