David Baddiel has been performing My Family: Not The Sitcom for nearly two years. And yet this exceptional show continues to develop and feels more pertinent than ever. As he points out, we live in an era of taking offence with alacrity. The Twitter jokes he's shared and the outraged responses that frame this performance presage his next show, Trolls: Not The Dolls, sustaining his flouting of the internet's first rule not to engage with keyboard abusers and online social justice warriors.

However, the tweets also serve as an introduction to Baddiel's flabbergasting family. The current case of comic Louise Reay's estranged husband suing her for material about their marriage has brought free speech firmly back into stand-up's spotlight. For various reasons that he expands upon, not least both his and his parents' lack of social filter, Baddiel has few qualms about washing their dirty linen in public. This is unquestionably his story to tell. And what a story it is, a loving tribute to his father and late mother that eschews trite sentimentality to portray them warts and all.

As recounted by his mother, a sleazy revelation about Baddiel's maternal grandfather, who fled the Nazis, was understandably dropped from the comic's episode of Who Do You Think You Are? But it rather nicely sets the scene for the jaw-dropping disclosures to come here. Never happier than when she was centre of attention (as a clip from Baddiel and Skinner Unplanned makes squirm-inducingly clear), Sarah Baddiel was an incorrigible performer all her life.

Conducting a decades-long affair with a golf memorabilia salesman, she was hardly discreet about her lover, with the brazen insouciance with which she conducted their liaison only properly brought home to Baddiel after he sorted through her effects. Although the fallout is all very comical (particularly the Oedipal complications of her lover also being named David), Baddiel is convinced it's had an impact on his mental health, prompting speculation as to how much he'll need to fuck up his own kids to turn them into comedians. Theirs is a saga that stretches all the way from the Holocaust gas chambers to Cristiano Ronaldo.

If the first half of the show is preoccupied with his mother's erotic escapades, the second shifts focus more towards Baddiel's father and his dementia. The condition is not so much robbing the old man of social awareness and civility as providing an excuse for the innate belligerence and inappropriate behaviour that he's always expressed.

There's obvious prurient interest in the intimate details that Baddiel shares, even if some of them are genuinely shocking. His fame, which he explored so richly in his last show, also threatens to hijack the narrative, obliging him to counter some reports in the press with further baring of his soul.

My Family: Not The Sitcom ought to make you grateful for the relative normalcy of your own kith and kin. But Baddiel truly brings his parents to three-dimensional life as flawed and exasperating, yet sexual and relatable human beings, leaving you in little doubt that love has overcome all. The nakedly confessional style he embraced for Fame and My Family will doubtless continue with Trolls and it makes for hugely compelling storytelling. Meanwhile, his perspective and appreciation of generational friction makes you question why Channel 4 passed on developing his recent family sitcom pilot.

David Baddiel: My Family – Not The Sitcom is on tour until Monday 2 July. Seen at Citizens Theatre, Glasgow.