Your two moon signs are 135 degrees apart (a Quincunx angle).
There may be a karmic lesson to be learned in this relationship. One of you may feel like you have to please the other, however this may be the sign of an imbalance in the relationship so take extra care to watch out for this in this relationship. Your Moon signs indicate that you are somewhat compatible: Aries is a Moon sign of high spirits and independent fire, whereas Virgo is a Moon sign of serious outlook and of quiet shyness.
Together the two of you get along ok. You may find that you cannot fully get along well in this relationship as the Aries Moon may feel that it cannot completely lead and be respected in this relationship, especially from a detailed aspect of feelings and emotions.