Definitely listen/ do everything that AKA_Monet and others have said, they are great ideas, and there are a lot of parents AND greeks on here, so they can give you a great perspective.
It IS hard when parents are against something that you love so much. My parents DID NOT understand why I put everything I had into my sorority. They know that I'm social and have a lot of friends, etc, but I almost always went above and beyond the call of duty (sometimes to the detriment of health, sanity and grades

).
My dad came and visited me my senior year, and actually stayed at my sorority house and absolutely loved my sisters, and even though he shook his head at me from time to time, he understood. My mom didn't come to visit me while I was in the sorority until I graduated. She met my sisters, hung out, etc and fell in love too. She also has a greater understanding of the benefits of the sorority because she is the VP of her teacher's union. She now understands what the cost is for the success of the organization as a whole. I am such a stronger person and a leader, rather than a follower, and I credit that to the sorority.
My point is, invite her to visit the house, meet your brothers, and hopefully she'll understand that it isn't about partying, it's SO much more than that. (community service, philanthropy, leadership training, connections, and brotherhood, etc

)
GOOD LUCK!!!