Your two moon signs form an angle of 90 degrees indicating a Square relation.
There may be many challenges in this relationship. A compromise is needed from one of you to overcome any hitches. You may share little understanding and opinion. Your Moon signs indicate that you are not particularly well matched.
Gemini is typically a Moon sign of sociability, charm and wit, and communication, while a Virgo Moon is very practical, modest, instinctive and usually quiet. The Virgo Moon would have to accept their silence in this relationship since the Gemini Moon will usually be very communicative and outgoing.