Melanie Griffith's recent admission to a rehab clinic isn't something husband Antonio Banderas is going to sweep under the rug.

"It's not a rumor, but let me explain to you," Banderas, 49, tells Ellen DeGeneres in an interview to air on Wednesday's The Ellen DeGeneres Show.

"It was said actually in some magazine that I said that I gave an ultimatum to my wife. That I present the matter of divorce because she has been involved in addictions and blah, blah, blah," says the actor. "Melanie has been addicted for many years and we always came out. We said it out loud. It was okay, we were never embarrassed of the situation but what happened she was clean and sober for six years."

But six years of clean living was endangered after Griffith, 52, had a skiing accident in Aspen, Co., a year and a half ago. Three operations in her knee required her to use narcotics – and come face-to-face with her demons again.

"In March, she came to me and said, 'I'm feeling a little bit weak in my determination for this ... so I just thought to go to rehabilitation by myself,' " Banderas said. "So the whole entire family is supporting her, and I am supporting her, and at this particular time more than ever. I'm very proud of her."

More than that, the entire family is actively participating in Griffith's rehab program.

"We have been following some type of therapy with other families," he said. "There are a number of invisible heroes working in AA all around the world. I just say to families, 'Don't get embarrassed, just confront this problem head-on. And don't hide from that because there is a beautiful gift at the end of this tunnel, and it is the person that you love back, and that is what I am searching for.' "

He added, "I am very proud of my wife."