Seconding The Sopranos. An incredible drama with very smart dialog and no shortage of humor. The malaprops alone are worth the price of admission.
I’m a little jealous. Wife and I are on our second time through, and I keep wishing I could be surprised like the first time.
Oh, I often start to watch some “quality” show but instead end up with a fun ensemble cast. Like just now, wife went to bed, I switched to Amazon Prime to watch Bosch… and instead clicked on “Chuck”. Also in that category: “Community” and “Arrested Development”… guess I love a good cast and how they play off each other.
“In Plain Sight” was another of the “Blue Sky” series.
“Jane the Virgin” & “Crazy Ex Girlfriend” I think they were both 4-5 seasons. They are genre shows that are very aware of their genres - and put “normal” people in the middle of crazy and mine comedy from the genre conventions and then have the space from the real parts - which allows them to handle both sides of the drama/comedy line. They’re very, very good.
For example:
it’s a silly fight, but (as I remember) the reasons for the fight make sense. If you find that funny, you might like the show.
Breaking Bad, and it’s spinoff prequel, Better Call Saul, are good.
I’ll also recommend White Collar. The premise didn’t appeal to me when it originally aired, but I gave it a shot on Netflix, and was hooked.
The Sopranos and Justified are maybe my top two recommends, with The Blacklist as well (it’s also on Netflix); James Spader seems like he’s having a hoot between being an Affably Evil Noble Demon and an Amoral Criminal Mastermind.
I think you might like Designated Survivor (3 seasons) or Bosch (6 seasons with another on the way).
Both Mrs. Mustard and I mourned when we finished them.
mmm
Netflix has Offspring, an Australian show that ran 7 seasons and meets your criteria. It focuses on a doctor and her slightly off kilter family. Highly recommended.
It also has subtitles if required for the non-Aussie speaker. 
I second most of the shows that have been suggested. One that I don’t think I saw above is House. Very good!
As I noted above, neither of us cared for Breaking Bad. I realize that puts is in a minority.
House was great. I remember watching Sopranos w/ our small kids - the youngest would say, “Anyone up for some totally inappropriate TV?” 
Jane the Virgin - we enjoyed for a couple seasons, then stopped.
Same w/ Orange ITNB.
Thought we’d like Veep, but stopped after a couple seasons.
I’ll have to check again for White Collar. I checked yesterday, and thought all I saw was a pay option.
Yeah - in sitcoms, we’ve loved Arrested Dev, Community, Parks/Rec, Kim’s Convenience, Curb Your Enthus …
Thanks for all the suggestions. Keep 'em coming!
Here’s another option. Very interesting family in a beautiful place before WWII
It’s common for BCS and BB to be considered together, but they really are different kinds of shows. They both have the same high quality, but their subject matter is very different. BB is very much about drug culture and violence, but BCS is really more about relationships with a little bit of drug culture in the background. BCS is an excellent show and should be judged standalone rather than as being in the vein of BB. My wife, who doesn’t like the violence typical in shows like BB, loved BCS. But it is more on the drama side of dramady, so not as light as some of the other shows being mentioned.
Gilmore Girls has like 8 seasons and a movie. And plenty of quirky characters to love or hate.
I prev mentioned we like BCS.
Gosh - my youngest used to watch Gilmore all the time! She’d never let us live it down if we started watching it.
Zach Galifianakis and Louis C.K. created ‘Baskets’ a few years ago, it was only 4 seasons, but it is the very definition of ‘dramedy’. Louie Anderson won an Emmy playing Mom Baskets. Its a…well, not quite a tragedy, but has moments of hilarity.
Older series, ‘House’, ‘Northern Exposure’ (already mentioned, yes) and ‘Desperate Housewives’ which went on for years. Going waaaaay back, ‘Days and Nights of Molly Dodd’ with Blair Brown, which might be streaming somewhere. Enchanting!
Also a good dramedy that only ran for four seasons: “Early Edition”. Dunno if it’s streaming anywhere but I think Netflix has the DVDs available.
So many great suggestions here, I think we’ll have to check out Monk and Baskets! 
Another one I highly recommend is Dead to Me on Netflix with Christina Applegate; only a couple of seasons so far but tons of both light and dark humor.
I also second Northern Exposure. Very quirky. I watched it when it was new and I was in my early 20s, then again a few years ago (mid-40s) and saw so much I’d missed the first time! How can you not love young weird DJ John Corbett?
I’ve long wondered about re-watching old shows. Hill Street Blues has come to mind. But I have had such mixed experiences - mostly bad - w/ older shows (pre-2000) not aging terribly well.
And we tend to be so “out of it” in terms of modern culture, that we are happy to try to watch TV shows that are at least from this century…
I’ve been contemplating re-watching Moonlighting for the first time since the original run.
A Place to Call Home. I avoided it for a number of years because from the photos it seemed like a sappy, happy family drama. I was so wrong! Oh the scandals.
Also:
Brokenwood Mysteries
Last Tango in Halifax
Madam Secretary
Started watching this on your recommendation, and you’re right, it’s good! The premise is a bit like Broad City, but the characters are original and the dialogue goes in some unexpected places.
I liked the first two seasons, when it was a drama about a Holocaust survivor. By the time they got through the third, it was just plain silly. They should have ended it when it said “The End.”