I am also married to a non-Greek. While I was in college, I dated several Greeks and several non-Greeks. As long as the significant other is respectful of the organization one is involved in, who cares?
My husband likes to joke around with me--for instance, he tells me Phi Mu is his favorite sorority, and every now and then begs me to tell him what AOT means (which of course is fun, because I will NEVER tell him)--but overall, he respects how much my organization means to me, and knows how much my organization has helped me through the years.