[Spy Kids] What countries did each parent belong to before they got together? Did one parent defect to the other side?

While the movie has latin american themes, it doesn't ever specify a country. From the first movie, the parents met after they were both sent to kill the other one. Eventually both parents are working at the OSS. Did one parent defect? Was this inter-agency drama?

If one parent did defect, which parent changed sides? This part of the movie was set late in the cold war, which opens up a lot of different ways this could go (unless it was stated explicitly somewhere).