They had fame, reams of money, and fans willing to do wild, unmentionable things just to breathe the same air — but in its September 24, 1971 issue, LIFE illustrated a different side of the lives of rock stars: Just like other mere mortals, it seemed, they often came from humble backgrounds, with moms and dads who bragged about them, fussed over them, called them on their nonsense, and worried about them every single day.

Assigned to take portraits of the artists at home with their sweetly square folks, photographer John Olson traveled everywhere, from the suburbs of London to Brooklyn to the Bay Area in California, capturing in his work the love that bridged any cultural divide that may have existed between his subjects.

Now, LIFE.com brings back Olson’s nostalgia-sparking photos — Marvel at the awesome decor! Gaze in wonder at the shag carpets and bell-bottoms! — and shares his insights and memories of hanging out with pop culture icons of the Sixties and Seventies, and their mums, and their dads.