The couple - who have been dating since earlier this year - reportedly dined with the 'Horrible Bosses' actress' dad John Aniston at Delmonico's Steak and Lobster House in Los Angeles three weeks ago, and the showbiz patriarch was "impressed" with her new boyfriend.
A source told Grazia magazine: "Jennifer is extremely close to her father, so it's important that he and Justin get along. At the meeting she was nervous because it really was a very special event for her.
"Thankfully, John was impressed with Justin, and it all went very well indeed."
After Justin's successful meeting with Jennifer's dad, the 'Mulholland Drive' actor is now said to be keen to introduce the 42-year-old actress to his own parents, Phyllis and Eugene Theroux.
The insider added: "Now that Justin has met Jennifer's father, he is desperate for Jennifer to meet his parents.
"He thinks they'll fall in love with her, especially his mother, because she and Jen have a similar sense of humour."
Just last week, the former 'Friends' actress met Justin's documentarian cousin Louis Theroux at exclusive London venue Shoreditch House, following the UK premiere of her new film 'Horrible Bosses'.
A source said: "Louis obviously approved of Jennifer. It looked like they were having a great time, and they all seemed instantly at ease with each other.
"Justin looked proud of Jen and seemed quite manly and protective."