The couple of 15 years "are very happy together," a source tells PEOPLE
Credit: INF

Are Antonio Banderas and Melanie Griffith on the brink of divorce?

Despite persistent Internet buzz that Banderas, 51, and Griffith, 54, are fighting to save their marriage, two sources maintain all is well with the couple of 15 years.

“They seem absolutely fine. Honestly, they seem happy,” a source who saw them together recently tells PEOPLE.

Rumors flew starting this spring, when Banderas, in Cancun to promote a new hotel, was photographed seemingly getting cozy with a blonde at a nightclub. Video has also surfaced of him dancing with actress Mallika Sherawat during a Cannes Film Festival party this year.

Last week, Griffith was spotted around town in L.A. not wearing her wedding ring, which caused more speculation about her marital status. But she’s also been spotted wearing her ring at recent events, including the Munich Film Festival in early July, which she attended solo.

Banderas “is in Budapest filming and they’ll be together again as soon as he’s done,” says another source close to the couple. “They really are very happy together.”

Banderas and Griffith have admitted their marriage isn’t perfect. In September 2011, the actor told AARP The Magazine he and Griffith “have had as many problems as anybody.”

The couple first met in 1995 while filming Two Much.

“I saw this sweet, vulnerable soul, funny, also very smart and generous,” Banderas recalls.

But their first meeting wasn’t as romantic for Griffith.

“The first thing he asked me was my age. I said, ‘That’s the rudest thing anyone has asked me first.’ But there was just something about him. Still is. I just love him.”