When the Smiths of Missouri – an all-American family with the regulation two blond children – posed for their Christmas photo, little did they know they would end up on a billboard thousands of miles away in the Czech Republic.

Just under a fortnight ago, a family friend of Jeff and Danielle Smith was travelling in Prague when he spotted some familiar faces beaming out of a poster advertising a grocery store's home delivery service.

He took a photograph and emailed it to his friends in St Louis – kindly translating the caption that promises "we will prepare and deliver your requests in two business days".

The picture was indeed of the admirably white-toothed Smiths and their two smiling children. Danielle had been so proud of the image taken by a photographer friend, Gina Kelly, that she had not only sent it out as a Christmas card to family and friends, but also posted it on her blog and other social networking sites, including Momlogic where she identifies her children as "sweet and sassy Delaney" and "loveable and crazy Cooper".

Danielle has expressed her surprise at the news of their international fame: "Interesting. Bizarre. Flattering, I suppose. But quite creepy."

The shop owner was equally shocked. Mario Bertuccio, who runs the Grazie store in Prague, said he found the image on the internet and thought it was computer-generated. He has promised to remove it and email an apology to the Smiths – and said if they lived nearer he would send them "a bottle of good wine".

In her blog on the Extraordinary Mommy site, Smith reflects: "So this is the price we pay for indulging in social media, I guess."

She had no idea the image could be used, she said, and would not have given her permission, but admits she was naive in putting up a high-resolution version on the website. She won't be doing that again – but said she would continue to post images of her family.

The smiley Smiths have now gone global. The site has registered 180,000 hits but Danielle writes that she is blocking the small percentage "who are commenting only to say that a member of my family (or all of us) are ugly".