Maybe this subject is moot these days but I don't see this much happening anymore these days in Sitcoms but in the 90's and 00's, occasionally a white character would be paired with a black character. Here I cover the rare main relationships and then the minor characters for just one episode. I will mostly cover African-American with White Americans. Because if you get nitpicky, you can call almost any couple interracial if Italian with British or Irish and Polish.
Saved by the Bell
Lisa and Screech
Screech was madly in love with Lisa and the subject of her being black and him being white never came up. She mostly was disgusted with him and didn't return his advances. Even if she didn't feel the same way and they were never an official couple, it was refreshing they made no big deal about them being from different races. Occasionally she would show signs of liking him back but it didn't happen much.
Saved by the Bell
Zack and Lisa
In one episode where Lisa was a fashion designer, Zack and her worked together closely and fell for each other. They ended up kissing, breaking Screech's heart. Again race was not an issue. This relationship was not brought up again.
That 70's Show
Hyde and Melissa
Hyde is attracted to Donna's radio work buddy Melissa (Reagan Gomez-Preston---voice of Roberta on "Cleveland Show"). They don't kiss or date, it is alluded that it will continue but we never see her again. We later find that Hyde is half-black but he doesn't date a black girl after this.
Alice and Alonzo
In the now canceled show "Mr. Sunshine," Alonzo (James Lesiure) and Alice (Andrea Anders) were a couple. James Lesiure is now on the TBS sitcom "Men at Work."
Crosby and Jasmine
Crosby (Dax Shepard) and Jasmine (Joy Bryant) had a kid together and then were engaged. They get married and have a second child.
A Fox TV sitcom in the 90's was about a blended family with a black father and white wife, two sons from the father and daughter from the mother. Lasted two seasons from 1990 to 1992. People said it was a bad show but I was 8 when it came out and I liked it.
Winston and Daisy
While Cece is Indian-American and has dated Schmidt who is Jewish and now seems to be paired with Coach who is African-American, I want to bring to light the rare pairing of Asian with Black. Daisy (Brenda Strong) was dating Winston only for a few eps and inadvertently broke up with him when he discovered she was seeing someone else. It was never mentioned about their different races even though the Schmidt character often mentioned him being Jewish and Cece being of Indian heritage.
Power Rangers Lightspeed Rescue
Joel and Angela Fairweather
In season 8 of Power Rangers in 2000, they had got in the habit of having new cast and story and Joel the Green Ranger was after the scientist Ms. Fairweather. She ignored him for the most part but ultimately he won her heart and they married.
James Gunn and Winifred 'Fred' Bruckle
In the end of season 3 and beginning of Season 4, Fred and Gunn became a couple. Like most couples in the Buffy and Angel universe, the relationship ended tragically. Gunn ended up killing for Fred and she didn't like that. She ended up kissing Wes. They broke up and next year Fred died. Anyway, their races wasn't mention but there was clear cultural differences.
Captain Ray Holt and Kevin Cozner
Ray Holt is a main character and we don't meet his husband until Episode 16. Holt's husband who dislikes the NYPD due to their treatment of Holt and his homosexuality during his earlier years on the force. He claims Holt is the 'funny' one in their relationship, while he is very stoic. Their races are quickly mentioned and what is emphasized is that Kevin is one of those pretentious smart gays.