It is much more common nowadays for couples to spend time apart while married, or even take their entire family abroad. However, if the marriage breaks up, however, there can be some difficult and unique issues, especially if one spouse is in the military. It is advisable to enlist a professional to help negotiate complex questions in this situation.
International divorces can be extremely drawn out, even if there are no children involved. Most of the common questions involve jurisdiction: if I am divorced in another country, will it be recognized at home? Whose law applies? What if my spouse is not an American citizen?