Jennifer Lopez and Marc Anthony Split
07/15/2011 AT 05:20 PM EDT
"We have decided to end our marriage," they tell PEOPLE in a joint statement. "This was a very difficult decision. We have come to an amicable conclusion on all matters."
"It is a painful time for all involved," the statement continues, "and we appreciate the respect of our privacy at this time."
Lopez, 41, and Anthony, 42, wed in June 2004 in a casual – and secret – ceremony at Lopez's Beverly Hills home.
They have two children, 3-year-old twins Max and Emme.