In January, one TV show swept the boards at the awards ceremony of the Israeli Film and Television Academy. It won five gongs. Small-screen buffs might assume that the recipient of all these accolades was Hatufim, the Israeli drama which – in its American remake – became Homeland. Not at all. Instead, honours rained on the bitingly funny and fearless sitcom Arab Labour (avoda aravit, a Hebrew idiom for a botched job). It came, says novelist Sayed Kashua, who created the comedy series with producer Danny Paran and still writes it as season four approaches, as "a nice surprise".

Arab Labour prods at every raw Israeli nerve. An example: the hapless hero Ajmad – a middle-class journalist and Palestinian citizen of Israel, much like his creator – goes into the local Big Brother house (in an effort to boost property prices in his block). The TV housemates have a task: one of them is not a Jew but an Arab. Can they tell which, and will Ajmad manage to "pass"? But if he's going to be a Jew, Ajmad insists, at least he ought to act like a cultivated Ashkenazi with a tragic Polish back-story and not some low-life Sephardic (Middle Eastern) oik. Imagine Chris Morris, Ricky Gervais and Sacha Baron-Cohen let loose together on the region's most open wounds, and you will begin to grasp the equal-opportunity chutzpah of Kashua's comedy. Maybe BB survivor George Galloway should take a look…

In 2004, Kashua had just published his second novel, Let It Be Morning. In it, a young Palestinian Israeli (part of the 20 per cent Arab minority within the state, rather than in the post-1967 occupied territories) returns to his village as an army curfew shuts it down. "I was playing on Sony Playstation, waiting to see what the critics would say," he recalls when we meet in London, where the Jerusalem-based author has come to speak at Jewish Book Week about his third novel Exposure (translated by Mitch Ginsburg; Chatto & Windus, £12.99).

Slowly, as he and Paran joined forces, the sitcom took shape. "In order to bring an Arab family into the mainstream living room, I knew that I had to use a lot of humour". After the first series, the Arab press gave him "a very hard time" over the self-sabotaging schlemiel Ajmad, very much a long-lost cousin of Larry – Curb Your Enthusiasm – David. Kashua does relish the viewpoint of the quizzically offbeat outsider: "I think it's a minority way of looking at things - of trying to survive and hit back with humour. 'Don't shoot me – I can tell you a joke!'"

His enemies attacked Ajmad as "a neurotic and not a hero. Which is true!" They protested: "When, finally, they gave us a series, this is what we're showing them? It's not 'gave us'. I worked very hard for this! And if you think you can make lectures on the Occupation for prime-time commercial TV, please go ahead and do it!" By now, laughter has done its ecumenical best and the series "works very well on both sides". Still, "there are no taboos". Arab Labour has dealt, for instance, with the 2011 law that criminalised the official commemoration in Israel of the 1948 nakba - catastrophe - of Palestinian dispossession: "We talked about that in a very painful episode of the second season."

Benevolent, blundering, Ajmad tries his damnedest but "never manages to fit into Israeli society". For Kashua, in life and in work, the effort - and the frustration - recur. He was born in 1975 in the village of Tira and grew up in a left-wing household, listening to his grandmother's family stories of the nakba and its aftermath: "It took me a while to understand what's called in Israel the struggle between narratives - how you must establish a narrative to create a nation". Aged 15, he went to an almost entirely Jewish boarding school in Jerusalem. He grappled with the Hebrew language, and devoured Israeli fiction and history: "It created a very strong feeling of the need to tell a different story."

He thinks this younger self "very naïve" to suppose that his alternative narrative could by itself change minds."I have a personal feeling that such stories can help better when there is a kind of understanding... between Palestinians and Israelis." Today, alas, there is a chilled deadlock.

About the Hebrew he deploys with such joy and audacity - "it's the language of the Bible; it's the language of the Occupation; it's the language of Zionism" - he still harbours mixed feelings. "On the one hand, this is the language that I use for writing, and in which I can express my feelings best… I have this illusion that Hebrew gives me some sort of freedom when it comes to writing... I wasn't sure I could write about love and drinking in Arabic. Perhaps God cannot read Hebrew." Yet for a Palestinian Israeli, "the Arabic language is the most important tool to keep your national identity". So does speaking in an "alien" tongue ever make him lonely? "When I look at things from above, it can be sad... But when I'm sitting down to write a story – no. These are the only tools that I have."

After studies in Jerusalem he worked on a local paper, while also writing short stories. At first, as a fledgling journalist, "I didn't think that my Hebrew was good enough. It was a friend of mine who said, 'Just write the way you talk.'" After a few years he broke into Ha'aretz, Israel's bastion of peacenik liberalism, as a satirical, story-telling columnist.

Dancing Arabs and Let It Be Morning, his first two novels, drew on aspects of his own background to mine the soul-deep dilemmas and divisions of Israel's Palestinian citizens. In Exposure, he deftly entwines the destinies of two complementary Arab protagonists. In one strand, a top West Jerusalem defence lawyer falls into a tailspin of rage, paranoia and self-hatred when – thanks to a note in a second-hand copy of Tolstoy's Kreutzer Sonata – he apparently finds evidence of his wife's infidelity.

In the other, a deracinated social worker – in a sort of existential counterpart to Ajmad's Big Brother adventure – takes on the identity of a paralysed Jewish man he nurses. For the young invalid's left-wing bohemian mother, "man was only smart if he was able to shed his identity". Neither alienated protagonist can ever do so. Strategies of assimilation and impersonation both come to grief in a cleverly interwoven intrigue full of startlingly acute observations of everyday Jerusalem.

Exposure proved a huge success in Israel, rapidly selling 80,000 copies. For Kashua, the "most important thing of all" came later. In general, he finds young Jewish Israelis "much more right-wing" than before: "They grew up with no hope… They have no faith in peace - on both sides. This is very, very sad." But, when asked by the Ministry of Education to nominate a novel to enter the curriculum as a set text, Israel's teachers of literature chose - Exposure. So the nation's schoolchildren will hear one – complex, subtle, darkly comic – version of the parallel story.

Kashua himself has three children, from 12 down to 18 months. As a family, they practise what they preach. Their daughter has just enrolled in a Jewish school. Yet as sectarian demagogues sway politics, he confesses "I'm really very scared… the fact that my wife and I are trying to teach them that all people are equal might be a big problem in the future, because it will hit them one day." Much of Israeli society "is not ready to accept such families". Whatever the barriers, exposure to his work - in print or on TV – may help to lower them: shock by shock, joke by joke.