What is the proper way to address a person who is an office in the military (USA) who at the same time has a Ph.D.? Would it be Dr. General John Doe or General Dr. John Doe?
Everything I've seen suggests that "General John Doe" without any "Dr." is correct (you've never heard of "General Doctor David Petraeus" right?); for example, military doctors are usually addressed using their rank, not as "Doctor." In part it just sounds clunky to try to use both titles. Similarly at Virginia Military Academy (bizarrely, in my opinion) all of the faculty are officers in the Virginia state militia, and are listed on the website with military titles (http://www.vmi.edu/Content.aspx?id=4294974313), not with the title "Professor" or "Doctor." I think "General John Doe, Ph.D." is more common, though discouraged in some sources I read. I think it's hard to go wrong just addressing someone in the military by their rank.
EDIT: I should probably say that isn't to say that you never combine Doctor with another title: "Herr Professor Doktor" is standard in Germany, (though I'm not allowed to call myself that, since I have a doctorate from the US) and "Reverend Doctor" (or even "Most/Right Reverend Doctor") are established titles, though more common in Britain than the US. Just in the specific context of military titles in the US, it's not standard to mix them with other titles.
CPT John Smith, Ph.D.; MAJ James Dean, M.D.; or LTC John Doe, J.D. are more correct when addressing doctorate officers in writing.
Although this is true that Military rank usually comes before academic in most cases, there are some exceptions.
Doctors in the Medical Corps are often addressed as "doctor." Many medical officers preferred to be called doctor as this title reflects their professional and client relationship instead of subordinate and superior. In addition, JAG officers are sometime addressed using the title of "counselor."