Missoni accomplished: Photographer Juergen Teller captures three generations of the Italian fashion dynasty

Florence, 1967: the models' underwear is clashing with their dresses, leaving Rosita Missoni with but one option: ask them to remove the offending items. Under the glaring lights of the catwalk, the jersey pieces become nigh-on transparent. The Missonis are asked not to return.

That, however, is far from the end of the story. The company that "started a knitwear revolution", according to Anna Piaggi, the former editor of Italian Vogue, has been going strong for more than half a century, and the secret can be seen in the photographs on these pages. Shot by fashion photographer Juergen Teller, they form the centrepiece of the Italian house's new ad campaign, which makes it clear that Missoni is a company that caters to women of every age. "It's a question of spirit: anybody can find a look in the collection," says Angela Missoni. Creative director and co-owner of the label with her brothers Vittorio and Luca, she's the daughter of Missoni's co-founders Rosita and Ottavio, and mother of Margherita, the latest in the line to take up the family cudgel, who came on board as a brand ambassador and accessories designer last year.

"Maybe people would like to have lunch with us," suggests 26-year-old Margherita, summing up the simple, if unconventional, appeal of the campaign. Unlike in most fashion advertising, she explains, where "you're meant to want to go out with the model", eating with grandma Missoni and her husband and two generations of their (grown-up) bambinos looks like a whole lot of good old-fashioned family fun.

The scene was shot by Teller at Margherita's grandparents' house in Sumirago (20 minutes north of Milan), and the family spent "a spontaneous day hanging out", she says. "It really represents who we are; the poses weren't studied." Close crops and angled shots convey both the family's energy and the kaleidoscopic play of eclectic objects, colours and patterns in the room, from the sofas to the knits.

The idea of focusing on the extended Missoni family at home plays to the brand's strengths; all the creative branding in the world couldn't invent its appealing heritage.

It was at the 1948 London Olympics that Ottavio Missoni, whose workshop was producing tracksuits for the Italian athletics team, met Rosita Jelmini, scion of a northern Italian family making women's clothing. They married and, in 1953, began making knits in a small workshop in Gallarate; five years later, they presented their first collection in Milan.

The dynamic, sporty quality of their knits was inspired by both nature and their collection of Modernist art. And just as the incident in Florence showed, the Missonis were not afraid to play outside the rules; their creations in wool, silk, cotton and rayon, too, have pushed boundaries. And while their patterns seem to evolve poetically of their own accord, they are scientifically charted during production. In 1969, when Diana Vreeland, editor-in-chief of American Vogue, first met the ' Missonis, she deemed their techniques "ingenious", saying: "Who said there are only colours, there are shades too!"

Rosita lost enthusiasm for fashion in the 1990s, but rather than sell the company, she recruited Angela as design director and the label has continued to flourish. Margherita has been a spokesperson for the brand for a while, but it was only last year that she really took an active, design role, after studying philosophy and then acting. With her glossy hair, natural beauty and free-spirited dress sense, she is frequently cited as a style icon: a poster girl for Missoni but also for a bohemian take on colour. An archive photo of the family clad in Missoni might suggest there was something of a house uniform while she was growing up, but, insists Margherita, "I was very free and built my own aesthetic. Vivienne Westwood used to work for us many years ago and I had a Westwood crown hat I would wear to kindergarten when I was about five. Obviously it was the coolest thing."

The clothes and accessories she wears in the shoot are from the spring/summer 2010 collection. She designed the 1970s-style sunglasses while Angela created the clothes, inspired by the idea of "Isadora Duncan and real modern girls going crazy in an Ibiza rave". The streamlined silhouette of layered crop tops, sarong-style woven skirts and hippyish trousers, in a carefree holiday palette of sand-coloured neutrals and aqua blues has a lighter, more youthful feel.

Which brings us back to the cross-generational message of the ads. For while Margherita might inspire younger clients, Rosita remains a role model for older customers. Her grandmother is indefatigable, says Margherita, who recounts the time she arrived home after a long-haul flight only to drive for two hours into the mountains to spend a day picking mushrooms. There's also no doubt who's the boss in these pictures. "She has an extremely strong personality," admits Margherita. "Who's the head of the family? My grandmother for sure."