Urban underwent surgery in November last year after a polyp was discovered on his vocal cords, resulting in the singer and Voice Australia coach being placed on voice rest for several weeks after his surgery.
Kidman told W Magazine that coping with the country singer's voice rest strengthened the couple's bond, saying: "It was sort of profound to go without his voice, and then to finally hear his voice. What if he sounded different?
"I was there for his first words, and then we cried. How many people experience their husband's first words? If that doesn't bring you closer, you're not breathing."
Kidman is currently in talks to play Grace Kelly in a project about Kelly's life in Monaco.
The 44-year-old actress is currently promoting her upcoming HBO film Hemingway & Gellhorn, in which she stars opposite Clive Owen.
Hemingway & Gellhorn is scheduled to broadcast on May 28 on HBO.
Watch a trailer for Hemingway & Gellhorn below: