My second favorite is Tony Soprano and his Mom…Livia…
https://www.youtube.com/watch?v=ed5BfnNXqqA
Skye/Daisy and Cal/Mr. Hyde on Agents of SHIELD.
Wasn’t she Aussie? That’s my fave, too.
Hello, Bubby!
I enjoyed watching the Draper family’s dysfunction on Mad Men. Don was a shitty husband and father, yet he and Betty had a bond that was never completely broken. I loved how he called her “Birdie” until the very end. And some of my favorite moments were between Don and Sally.
I forgot another obvious choice: The Bundys from Married with Children. So much fun viscious snark covered up the fact that they loved one another.
In Boardwalk Empire Jimmy and Gillian Darmody’s relationship was hard to beat for pure pathology. For that matter, Gillian’s relationships with just about every other character she had anything to do with were also fucked up, especially Nucky and the Commodore.
Moonlighting?
Thats a great choice…on and off set. Wish the producers had held off on the consummation, it killed the show.
She was supposed to be Aussie but her accent always struck me as south of England. And the way she said “Bobby” was mad sexy.
Freddie and Stuart in Vicious.
Homer and Marge Simpson specifically, but Homer and everyone in general. He just wasn’t capable of a normal relationship with anyone.
Come to think of it, EVERYONE on The Simpsons was in a dysfunctional relationship with every single person they knew. 
Thus its hyper-reality. 
Flanders had a good relationship with his wife until she died. Then the problems began.
ETA: My submission would be Mitch and Cam on Modern Family. That is not a healthy relationship.
Niles and Maris on Frasier, especially since so much of the awfulness of Maris was left to the viewers’ imaginations. She’s one of the best invisible characters ever created. And David Hyde Pierce’s brilliant delivery and physical comedy gave our imaginations so much to work with.
Reminds me of Carleton the Doorman on MTM. There’s another guy who had a dysfunctional relationship with everybody.
Speaking of Livias - the relationships in I, Claudius between Livia and absolutely EVERYONE were deliciously twisted. I loved her warning to her son Tiberius about Augustus’ personal fig tree… “Don’t eat the figs”.
And my favorite historical dysfunctional family, the entire Plantaget brood in The Lion In Winter. “What family doesn’t have its ups and downs?”
Saul trying to understand Carrie on Homeland.
Odo and Quark.
Sam and Dean Winchester.
Mal and Inara.
I don’t watch drama’s unless there are lots of special effects.
Sam and Diane on Cheers. I’m tempted to say Carla and her scuzzy husband too, but they seem oddly perfect for each other.
Yes, yes, a thousand times yes! And Frasier and Lilith’s relationship, too.