Inside Michael Douglas and Catherine Zeta-Jones's Struggle to Save their Marriage

By Michelle Tauber

09/28/2013 at 01:45 PM EDT

Michael Douglas and Catherine Zeta-Jones

Plenty of stars would balk at facing a red carpet press gauntlet in the midst of painful personal problems. Michael Douglas is not that kind of star.

Looking healthy, dapper and upbeat, the consummate Hollywood pro showed up for the Emmy Awards on Sept. 22 ready for the spotlight. With his wife of nearly 13 years, Catherine Zeta-Jones, more than 6,000 miles away at a film industry event in China, Douglas didn't shy away from questions about the "break" the couple recently decided to take from their marriage.

"We're working things out, talking," the star, who took home a trophy for his performance as Liberace in Behind the Candelabra, told PEOPLE, "and we'll see how she goes."

For Douglas, 69, and Zeta-Jones, 44, the decision to separate this past June was wrenching. Four months later they're still trying to decide whether their marriage can – and should – be saved.

"They're not giving up," says a source close to Zeta-Jones.