No interracial relationships:
Television history was made in the original Star Trek series, which featured the first interracial kiss on television, when Captain Kirk kissed Lieutenant Uhura.
Although there may not have been more than one representative of another ethnic group on the bridge of the original Starship Enterprise, there were several people of different nationalities (most notably a Russian, note that this was in the middle of the Cold War). That's not something you see a lot on modern American television shows: any non-US-ian is most likely a shallow caricature.
All this is offset, however, by the sexism of the women officers' tight space suits.