Jennifer Lopez and Marc Anthony Split

07/15/2011 at 05:20 PM EDT

After seven years of marriage, it's over for Jennifer Lopez and Marc Anthony.

"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.

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They have two children, 3-year-old twins Max and Emme.

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