Sorry, transferring aircraft isn't implemented yet. When it is, it will essentially work like an attack, where those jets, missiles, or bombs are set to transfer to the other airbase that night instead of attacking that night.
When you capture an enemy airbase, everything within it is destroyed (under the premise that a country would destroy their equipment before letting an enemy take it over). I actually contemplated programming it so that any nukes in a captured airbase would immediately detonate, but I decided against it.