The 'Pushing Daisies' actress - who has been dating the 44-year-old actor since the beginning of the year after meeting him on the set of new TV movie 'Neverland' - is smitten with the 'Notting Hill' star, and he even gets on well with her six-year-old daughter Gracie, who she had with her ex-partner of 10 years David Thewlis.
She said: "I think one of the things that draws us together so much is our need to feel safe. You know, everyone has to go out there and face the massive wide world and face rejection and it's nice to have a sanctuary and a place to go and a pair of big arms around you and someone to say, 'Oh, you're all right'.
"He is brilliant with Gracie. We introduced her to the idea really gently and softly. The good thing is, she had seen him on the set of 'Neverland' and she said, 'You are very nice friends. I think he's very nice.' "
Anna and Rhys - who have a three-week rule to limit their time apart from each other - also have chemistry in the kitchen, where they have often have midnight "cook-offs" after a heavy night out.
The 35-year-old brunette beauty added in an interview with Tatler magazine: "Rhys knows I like things simple but actually he's the most amazing cook.
"We cook together. We often have midnight cook-offs if we've been out and we're both hungry. It's like 'Ready Steady Cook'. We hardly watch TV but if we do it's loads of cookery and travel programmes."