Your two moon signs form an angle 90 degrees apart (a Square).
There may be many challenges in this relationship. A compromise is needed from one of you to overcome the grating feeling you may have on each other. You may share little understanding and opinion, especially from a feeling aspect, 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.