I normally retreat to BBC3 for comedy comfort food – Gavin and Stacey repeats, Russell Howard showing pictures of baby animals – so I was surprised when a hilarious slice of the surreal caught my attention. The six-part comedy Cuckoo isn't just another "boy-meets-girl-meets-family" show with vague overtones of My Family Christmas specials. Instead it resuscitates the suburban sitcom, wheels out the tropes … and then projectile vomits all over them like a middle-England dad whose son has accidentally peddled him ecstasy (see episode three for details).

Saturday Night Live alumnus and Lonely Island singer Andy Samberg is well known in the US for offbeat TV (Portlandia, Parks and Recreation), but Cuckoo is his first UK role. He's the hippie stoner of the title, whose demonstrative behaviour and ranting rile new father-in-law Ken (Greg Davies). He is neither a doctor nor a lawyer nor an Aston Villa supporter as his spouse's dad would have preferred, but having met somewhat dippy Rachel on her gap year, he has moved into her family home in the Midlands and bought a van from which he plans to sell baked potatoes. (Don't ask where he got the cash.)

Much of the comedy is derived from the dynamic between Ken and his irritant son-in-law, who has won the hearts of the female members of the Thomas family by pontificating about life and using Shreddies as a metaphor for love. And although the first episode was rather clunky, a slow start doesn't seem to have harmed Cuckoo's potential for laughs: with the bonds (or lack thereof) between the characters now fully established.

As if the clash between Cuckoo (whale music, nude meditation) and Ken (would-be local councillor, Nazi history enthusiast) wasn't enough, exchanges between Ken and wife Lorna (Helen Baxendale) are toe-curlingly embarrassing, too. While there are touches of Mr Gilbert, the authoritarian Inbetweeners headmaster in Davies's "dad" act, he is also protective of his rather naive wife and they work well together. Then there's Dylan, as played by Outnumbered's Tyger Drew-Honey. Here, his character schemes, swears at this parents and lets his dad take his aforesaid ecstasy pills in lieu of Nurofen to avoid fessing up to buying drugs – all with a face like a bulldog being given an enema. He's the perfect moody teen.

It's the uncomfortable situations – Ken being accused of perving over his son's teenage love interest; said girl's dad meekly hurling a chicken drumstick at him in protest; creepy student Zeb serenading Rachel à la Nicole Scherzinger; Cuckoo making sexual comments about Rachel in front of her dad – that make this show so watchable.

The potentially predictable is given a new edge of awkwardness thanks to the cutting dialogue and the timing of Davies and Samberg in particular. When their adversarial characters Cuckoo and Ken became best pals after some drug-fuelled bonding, the plot feels familiar but the execution fresh. Cuckoo isn't turgid and scenes don't outstay their welcome, with every half-hour episode managing to pack in plenty of twists.

Last week's episode contained a large and welcome dollop of screen time for Samberg as Cuckoo joined the family on a trip to visit granddad, tried to administer "birthday bumps" and conducted an experiment to find out whether a cat was the reincarnation of grandma Debra. It played to all of Cuckoo's strengths: satirical yet sentimental, prosaic yet potty.