When the relationship first became public in May 2000, the headlines were harsh. The mayor shortly announced that he was divorcing his second wife, Donna Hanover, and he was forced to respond publicly and defend his new relationship, saying, "Judith Nathan is a very, very fine person. She's been a very good friend to me."
The fact that the mayor was still married when they met made the beginning of their relationship a "rocky road," but Judith says that "when you have a partnership that is based on mutual respect and communication, the two of you know what's going on."
The couple soon faced an even bigger challenge, when Rudy was diagnosed with prostate cancer. He was in the midst of a heated Senate campaign against Hillary Clinton; he dropped out of the race soon after receiving his diagnosis.
"I was petrified in the beginning, of course, yes," Judith said of the fear that he might not survive the cancer. "While I tried not to let on to him at that time, that, for me, was one of the most frightening days of my entire life. And, as we all know, he's cancer-free now, thank God."
Sept. 11 introduced Rudy to America and the world, and changed many people's views of him. Judith said it changed him as well.
"I was there with Rudy shortly after the second attack. … And remained with him throughout the next several days," she said. "And the things that we saw, Barbara. … Unspeakable horrors. … There isn't [any] human being that could possibly go through that experience. … And not be changed."
Judith was constantly by the mayor's side during the aftermath of the attack. Asked whether she thought she was helpful, she replied, "I hope so. We'll let him answer that."
Rudy did answer that question, when he joined the interview to talk about the woman he clearly adores.
"Nobody will ever know all the things she did to get me and the city through Sept. 11," he said. "She said, 'I'm not leaving your side.' And I said, 'OK, well if you're going to be here, you're going to go to work."
He put Judith in charge of getting information from all of the hospitals. She helped deal with the victims' families and also helped start the Twin Towers fund.
Sept. 11 helped them put things in perspective, but it was not the end of the couple's personal challenges. The dissolution of Rudy's marriage continued to attract attention. When asked whether Judith was responsible for the breakup of his marriage, Rudy told Walters, "She was not."
"I tried to keep that all as private as possible," he said. "I think I should be very, very clear that she was not the cause of the breakup in any way at all."
"We love each other very, very much, and we developed a wonderful relationship," he said. "And she's the light of my life, and she's the person that got me through the most difficult times of my life."
As for all the scrutiny, Rudy said, "This is part of the price you pay for being a public official, a public person."
Judith acknowledged that it was "difficult" to be thought of as the other woman, especially because she was a single working mother.
Walters asked Rudy whether America had reached a point where divorce, or a number of divorces, was not important in electing a president.