For me the issue was my husband's age, he's 15 yrs my senior. My mom did a lot of talking, usually in the "he's so much older" line. She's not outspoken like your parents are, instead she uses the "guilt trip"!! eeeeek!
We too had a long friendship at first, with a love that gradually increased and deepened over time. We've been married just over 3 yrs now, and that deepening just continues. It's not something you should give up.
What I finally had to do is step back and allow my parents their worries and upsets, and leave them to deal with them alone. NOT EASY!!!! BUT, it was worth it. It took time, age worries gave over to jealousy (especially my mom) and then to just hidden resentment. But as I forced that distance to remain they started to deal with it, and are now understanding of the fact that he is the best "choice" I could have ever made for myself. I encourage you to do the same. Let your sweetheart know what your doing and rely on him for support, you'll need it. There will be anger and tears, but by staying firm you allow them time to deal with all this change. It's more about their baby girl then the ethnicity then they'd like to admit. Saying a "I'm sorry, but this is the choice I've made." and not speaking about it is the best course. Expect them to be angry about the forced distance in this issue!! Mine were horrid!! But they got better, starting with my dad, and gradually began seeing things for what they really were (empty nest syndrome).