The Queens Of The Stone Age rocker and his Spinerette singer wife - who have a three-year-old daughter Camille Harley Joan together - have duetted on some of their favourite songs but Brody admits their studio sessions are unlikely to ever see the light of day.
She said: "Josh and I have done a few covers together. We've recorded a song by Creedence Clearwater Revival, they are just one of the coolest bands ever.
"I doubt we'll ever get chance to release a covers album though because our schedule is so crazy."
Brody has teamed up with Al Johannes for Spinerette's forthcoming album and says the record runs through a wide range of topics, including birth and death.
She explained to BBC Newsbeat: "The album deals with the two juxtapositions of death and birth," she explains.
"It was pretty heavy because Alan's wife was diagnosed with cancer a couple of months before we started recording.
"My dad also died so I kind of got lost there for a minute.
"So recording this album was therapy for the both of us because we had a place to go which gave us some hope."