In Western astrology, the Moon signs are not used to interpret the compatibility between a couple. Only the Sun sign compatibility is used, the simple reason being the Sun is the all powerful energy source among the planets. The Sun is all about our ego, self-expression and will power. It has nothing to do with how compatible one is with his or her partner.
Our feelings, emotions and security needs are all ruled over by the other luminary, the Moon. Hence it is better to say that compatibility is all about the Moon. The position of the Moon in our natal chart indicates that area where we feel at home and hence Moon compatibility between two individuals is a must and the best to look up to when they start to live together.
Here is a general guide for the Moon sign compatibility between you and your partner.
Don’t know your Moon sign, Find it here