Thieves made off with four-year-old cocker spaniel bitches Skyla and Lady, as well as a quad bike, tools and farm machinery in the 2am raid.
The home owner gave chase in a pick-up truck as the thieves escaped across fields to the rear of his home in The Street and on to Wheatley Lane.
His pursuit came to an abrupt end, however, after getting stuck in a ditch.
The family are now offering a £1,000 reward for any information that leads to the recovery of their pets, both of which are microchipped.
Friend Sue Vincent has helped set up the family’s appeal, and to-date her posts to various dog and horse communities on Facebook have been shared more than 3,000 times.
Sue told the Herald: “They are devastated as the dogs were part of their family. They can’t sleep, they’re out looking in the car all the time. They’re absolutely gutted.
"The thieves came in across the fields to the back of their house and through the next door neighbour’s garden after breaking down a fence panel.
"They nicked a quad bike, all sorts of machinery and tools, and then the two dogs out of their kennels – and then they went back across the fields.
"There’s tracks across the ploughed field and then they got onto Wheatley Lane and got out towards Kingsley Way and off.
"The owner did give chase in his pick-up truck but bless him he got stuck in a ditch, which is probably just as well to be honest.
"The dogs are both microchipped – so if they sell them on and some poor, unsuspecting family buys a lovely dog, and then they have to take it to the vet for whatever reason, it will get scanned and the chip company has logged the both the dogs as missing now stolen.
"So that would come up and then they would contact the owners. And hopefully would be reunited that way – but they would have to be scanned first for that to happen."
Sue added the police have visited the family, and are investigating. Anyone with information is asked to call Hampshire Constabulary on 101, quoting crime reference number 44200135447.
Sue continued: "I mean, nicking tools and stuff, we’re used to that around here. Sadly, garages get broken into quite often because it’s quite rural. And we all back onto fields so it’s quite probably easy for thieves. But nicking your dogs is another another thing."
The family have asked for anyone with information to call them on 07785 567743 or 07787 225369.