"I'm in a constant state of worry about my career," says Moore. "I have always have been because you never know. You never know if you're going to get another job. You don't know if you're going to be able to keep doing what you want to do."
She told CBS News Sunday Morning Correspondent Rita Braver that she just needs to hope and keep looking for work to sustain her career.
But lately, 42-year-old Moore has found material that any actress would envy. They are roles that have earned her two Academy Award nominations — one for Best Supporting Actress for her "The Hours" role and the other for Best Actress for her part in "Far From Heaven."
It's the first time in 9 years that any actor or actress has received the double distinction.
In "Far from Heaven," set in the 1950s and shot in the style of a '50s melodrama, Moore is Cathy Whitaker, a housewife who learns that her husband, played by Dennis Quaid, is homosexual. She then launches her own affair with an African-American landscape company owner, played by Dennis Haysbert.
"I love [Cathy]," says Moore. "She's incredibly tolerant and sort of forward thinking. She's almost an American idealist."
Director Todd Haynes says he wrote the "Far From Heaven" role for Moore because she enchanted him in an earlier collaboration.
"She's incredibly charming, funny, intelligent, easy-to-be-around person, without a huge ego and with a very caring quality," says Haynes. "She comes with all the charms and charisma most movie stars have, but it's not the mainstay of her character. She really re-invents them from scratch each time."
But that doesn't mean Moore doesn't get in a tiff sometimes.
"I used to fight with our costume designer, Sandy Powell, and say, 'You know, Jane Wyman never carried a purse,'" laughs Moore. "I'm not going to carry a purse. You know, Jane Wyman was always running out the door with nothing in her hand. I thought: 'Well, you know, if that's the contention of the time, then that's what I'm going to do.'"
In "The Hours," Moore plays another '50s housewife. But she says the comparison between the characters she plays is frustrating because "The Hours" character she plays is someone who wants to be in the book she's reading and escape her reality.
The woman is depressed and abandons her family.
"The knowledge of what she's done has stayed with her for every single day for the rest of her life, and it's excruciating," explains Moore. "The horror of knowing that you have done that to your children … I mean, I'm going to start to cry. It's terrible.
As a mother, Moore was especially hurt by her character's action. She says she always get emotionally involved with her characters.
"That's the nature of acting," says Moore. "That's what I like about it."
But Moore, the daughter of a military judge and a social worker, did not always see herself as movie star material.
"I was the kid with the glasses who was very thin," says Moore of her self-proclaimed geek years.
But by the time she went to high school and college, the beauty and the talent started to shine through.
She says her parents encouraged her to go to college because if her acting dream didn't become a reality, she could go to graduate school and then get a "real job."
After college, Moore moved to New York to break into acting. But, she says, it wasn't easy.
"It was like I was chipping, chipping … with a hammer," says Moore
In 1985, she broke through. She landed a part on the soap opera "As the World Turns," playing two half-sisters, Frannie and Sabrina.
"Strangely, we had the same father and our mothers were sisters, which is kind of disgusting," laughs Moore.
She won an Emmy for the role, then moved on to theater and, finally, films. She has worked in 33 movies, playing everything from Hugh Grant's pregnant girlfriend in "9 Months," to a scheming blackmailer in "An Ideal Husband," to a scientist in the "The Lost World," the blockbuster sequel to Stephen Spielberg's "Jurassic Park."
She picked up Oscar nominations for Best Actress in "The End of the Affair" and Best Supporting Actress (playing a porn star) in "Boogie Nights."
But it was her role as a member of an unhappy family in "The Myth of the Fingerprints" that brought her happiness off-screen. She fell for director Bart Freundlich the first time she met him.
"Then we started to see each other and then we stayed together," says Moore. "It's embarrassing … because you never want to be the actress that has an affair on the set."
A lot of women may be interested to know that Freundlich is quite younger than Moore.
"He's nine years younger than I am," says Moore. "Physical age and psychological age are so different things. And for us, I think we found that we're pretty much in the same place, and it's okay."
They have two children, and have recently become engaged. Now, there are those two Oscar Nominations to contend with.
She says winning an Academy Award would matter to her.
"If I told you that I didn't care, then I would be lying," says Moore. "I'm always glad when I win something."
But win or lose, Julianne Moore's name is a household name. And as for her worries about finding work, she already has a new film in the works.