There's a moving, first-person account in today's Guardian about a British-Pakistani man who married a white, Christian woman despite his family's insistence he marry Muslim.
His mother gave the wedding her blessing to his face, but then complained behind his back to siblings. Next she was declining her invitation, and the rest of the family followed suit. At the last minute, a sympathetic sister convinced their mom to come. They planned to stay just for dinner, but they closed the place down at 1 a.m.
A heartwarming ending for a story with such a volatile beginning, so I feel pretty confident it's possible for even the most traditional families. If you've been in a serious, interracial relationship, tell us how you either worked your way in to his family, or persuaded your own to like, love, or just tolerate him enough for a Sunday dinner.