Your two moon signs are 135 degrees apart in a Quincunx angle.
One of you may feel like you are constantly working to please the other, this may be the sign of a relationship that is out of balance so take extra care to watch over this in the relationship.
You may not share much understanding, especially from a feeling aspect, your Moon signs indicate that you are not very well matched. Gemini is typically a Moon sign of sociability, charm and wit, and communication, while a Capricorn Moon is efficient, hard-working, serious and sometimes extremely cautious. The Gemini Moon would have to accept the serious side of Capricorn in this relationship and the Capricorn Moon may have trouble accepting the charming childishness of the Gemini.