The angle between your signs — the square (90°)
The square is the aspect of tension: you want the same thing at the same time, just not the same way. This bond never falls asleep. It asks you to pick your battles, and makes you both stronger when it holds.
Your elements — Air and Earth
Air thinks, Earth makes it real. One has the ideas, the other knows how to make them stand. Translation is often needed: you do not measure time the same way.
Your rhythms — mutable and mutable
Two mutable signs: you both adapt. Anything is possible, nothing is set — sometimes someone has to decide.
Your rulers
Gemini and Virgo are both ruled by Mercury: words and wit, lived in two ways. The same engine, two ways of running it.