Describing the 29-year-old as a "wonderful young man", Fiona Jones said it was "very unlike him" for leaving without saying a word to any of them.
The father-of-one, who works as a rubbish collector, was reported missing by Derbyshire Police on Saturday (December 12) and was captured on CCTV in the shop Boyes in Matlock at around noon.
Fiona, of Darley Dale, said: "He's a wonderful young man, brilliant father, husband. This is so unlike him...it's just not like him at all.
"He's a loving family man. He's got a two-year-old son, and absolutely adored his son. He's got a loving, supporting family around him and I can't understand why he is not in contact with anybody.
"He's got his mum, his dad, his sister or his grandparents.
"Just come back, Josh. We're all just absolutely beside ourselves. Frantic, we're worried."
The 49-year-old care worker said the family are left devastated since he went missing, especially his wife.
"She's a bit like me. One minute, she's calm, one minute, she's absolutely in pieces. I can't describe how I'm feeling.
"Everyone that needs him and that knows him all loves him. He's brilliant, people gravitate towards him. He's got one of those personalities where people just like to be with him.
"He's a very sensitive young man," she said.
Fiona said the family have been going around town to show pictures and spread the word on his missing son.
"I just went out from the local area, showing pictures of him so people can look out for him...we're just tearing our hair out. We feel helpless, we can't do anything," she said.
The police have previously received numerous sightings of a man matching the description of Joshua on the A632 heading towards Chesterfield at around 4pm on the day he was reported missing.
It is believed the man was trying to hitch a lift and officers were keen to speak to those with information, in order to narrow down whether the man seen was Joshua.
Those who have seen Joshua or have information are urged to contact the police, quoting reference number 518 of December 12.