Mel Gibson hits the red carpet with girlfriend

More than two weeks after his wife filed for divorce, a smiling Mel Gibson made a rare public appearance with his girlfriend Tuesday night at the L.A. industry screening of "X-Men Origins: Wolverine."

"Mel has been single for almost three years and it's nice to see him getting out and enjoying himself," his rep tells PEOPLE exclusively.

The actor, 53, dressed in a black suit with a dark gray shirt, stepped out with Oksana Grigorieva, a 39-year-old Russian signer signed to his record label, Icon Records. The couple held hands as they walked the carpet before taking a seat at the screening at Grauman's Chinese Theatre in Hollywood.

"They came in quietly and as under-the-radar as they could and they were pretty low-key," says a source. "Mel seemed very comfortable."

According to the source, Gibson attended the screening at the invitation of Fox chairman James Gianopoulos and "Wolverine" producers Richard and Lauren Donner and fellow Aussie Hugh Jackman, who told the audience that he got inspiration for his character from Gibson's role as Mad Max.