Neither representatives for Willis nor Moore immediately responded to Fox News' request for comment.
Willis is now married to Emma Heming and the couple share two daughters, Mabel Ray, 8, and Evelyn Penn, 5.
In the photo, the entire family, including their pets, are wearing same striped pyjamas with daughter Scout, 28, holding her leg up and Tallulah's boyfriend film director Dillon Buss in the background.
"Chaotic neutral", Tallulah captioned the image.
Tallulah previously responded to a comment on the matching shot of her parents, explaining how her family made a decision to social distance together. Bruce later married Heming Willis in 2009.
Lady Gaga has announced she is partnering with Global Citizen to put on a special concert, One World: Together At Home, which will benefit the COVID-19 solidarity response fund.
Demi has been keeping the family together during social isolation, uploading a pic of her and her daughters surrounded by photo albums, singing and occasionally doing tricks like balancing a dog on her head.
Despite divorcing in 2000, Demi and Bruce have stayed close.
The Ghost star went on to admit that the couple "felt more connected than we did before the divorce".
"I think Bruce was fearful at the beginning that I was going to make our split hard, and that I would express my anger and whatever baggage that I had from our marriage by obstructing his access to the kids - that I'd turn to all of those ploys divorcing couples use as weapons", she wrote.