Sheen says he loves his life on '20/20'

Charlie Sheen animatedly discussed his polyamorous living situation, his children and the cancellation of his CBS show "Two and a Half Men" on ABC's "20/20" Tue. night.

Sheen's two live-in girlfriends, Natalie Kenly, a graphic designer and Rachel Oberlin, a porn star, who he refers to as his "goddesses" also appeared on the program.

Natalie Kenly and Rachel Oberlin

The troubled actor allowed ABC's cameras into his house this weekend, where Sheen talked about the public's perception of him.

"They can't process me because it doesn't make sense because I'm not normal and they're normal," said Sheen.

Sheen blamed the sleeping medication Ambien for his breakdown in New York last Oct. and admitted to being an insomniac.

"I don't sleep," said Sheen. "I wait, I sleep on cars, on couches, I sleep when I can."

He also said he was drug-free and later passed a drug-test.

The actor wasn't shy about his love for porn stars.

"You already know what you're getting before you meet them."

While Oberlin said she would love to marry Sheen, the actor admitted he has no immediate plans to marry again.

"I tried marriage. I'm 0 for 3 with the marriage thing. So, being a ballplayer -- I believe in numbers. I'm not going 0 for 4. I'm not wearing a golden sombrero," he said.

He did, however, declare his fondness for his two girlfriends.

"These are the women that I love that have completed the three parts of my heart," said Sheen.

The actor has no qualms about exposing his two sons to his unconventional living arrangement.

"I'm not gonna worry about it, or I can say, 'Hey, kids, your dad's a rock star. Look at his experiences. Look at what he survived,'" said Sheen.

Kenly said, "I love those boys. I would take a bullet for them."

Sheen also spoke about "Two and a Half Men" creator Chuck Lorre.

"It was a fake friendship," said Sheen. "I never felt respected in a way that I should have been."

Sheen also updated his newly-minted Twitter account Tue. evening, posting:

"Just got invited to do the Nancy Grace show... I'd rather go on a long road trip with Chuck Lorre in a '75 Pacer.... "

He also tweeted, " Winner..! 2012...," posting a photo of himself holding an image of his head superimposed on an Oscar trophy.

Earlier today, CBS president Leslie Moonves broke his silence on Sheen, saying Sheen has been "on the air quite a bit these days."

Moonves also poked fun at the actor's media blitz.

"I wish he would have worked this hard to promote himself for an Emmy."