At first glance, I think your Gemini Moon and your partner's Aries Moon are great together. The Moon rules our emotions, and Aries and Gemini are Fire and Air, which work well in a relationship. If we think of the elements, fire needs air to burn! Gemini moon people are verbal about expressing themselves, they want to dicuss everything, write poetry, engage on an intellectual level. Aries moon people fall in love fast, and tend to put loved ones on a pedestal. So your partner is quite open about "showing you off" to friends and may even compete with you a little! Both love in a light and breezy kind of way, and it works well. Your Leo Sun means you like to be the center of attention, and will be upset if you aren't getting enough. But with an Aries Moon person, that shouldn't be an issue. You are strong willed and like your own way. A Virgo Sun is an Earth sign, down to Earth, and sensible. They care about health, diet, and exercise. They will want to take care of you. Virgos are more retiring than Leos, but can be a calming influence on you. Both Gemini and Virgo are ruled by Mercury, so you do have a strong mental bond. I think there is enough good here to get along well so that you don't have to try too hard to be compatible, you just will be!