Gwyneth Paltrow and Chris Martin ''held hands'' at Robert Downey Jr.'s recent birthday bash.

The former couple, who announced their split last month after 10 years of marriage, are determined to stay close friends and put on a united front as they stepped out to celebrate her 'Iron Man 3' co-star's 49th birthday party in Los Angeles on April 6, with their children, Apple, nine, and Moses, eight.

A source told PEOPLE magazine: ''They held hands and were playful and laughing.

''No one said this was an ugly situation. Showing themselves to be a family is very important to both of them, and that won't change.''

The blonde beauty, 41, and the Coldplay frontman, 37, have gone out of their way to prove their split is amicable and took a holiday to the Bahamas shortly before news of their separation was announced on Gwyneth's lifestyle website GOOP in a post titled ''Conscious Uncoupling''.

They wrote: ''It is with hearts full of sadness that we have decided to separate.

''We have been working hard for well over a year, some of it together, some of it separated, to see what might have been possible between us, and we have come to the conclusion that while we love each other very much we will remain separate.

''We are, however, and always will be a family, and in many ways we are closer than we have ever been.''