Actress Kate Winslet says she aims to maintain privacy and refuses to accept that her family cannot lead a "relatively normal life".
Kate, 37, was speaking after a High Court judge said a tabloid newspaper could not print "innocent but embarrassing" photographs of her husband Ned RocknRoll, 34.
The Sun argued that publication of the "semi-naked photos" was justified because Ned - who changed his name from Abel Smith and is a nephew of tycoon Sir Richard Branson - is a "public figure".
But Mr Justice Briggs ruled against newspaper bosses following a two-day hearing at the High Court in London. He said he would give reasons for his decision at a later date.
After the hearing Kate and Ned issued a joint written statement.
"We have stopped The Sun from publishing semi-naked photos of Ned taken by a friend at a private 21st birthday party a few years ago," said the statement.
"The photos are innocent but embarrassing and there is no reason to splash them across a newspaper.
"We recognise that in the internet age privacy is harder and harder to maintain. But we will continue to do what we can, particularly to protect Kate's children from the results of media intrusion.
"We refuse to accept that her career means our family can't live a relatively normal life."
Ned argued that there was no public interest in The Sun publishing the photographs, taken more than two years ago at a private fancy dress party with an "outrageous" theme. He said he was not a role model and was a "relative nobody" before his marriage to Kate.