The family, on their way through Switzerland, were driving down from the Forclaz pass towards Martigny at around 10am on Saturday when the driver pulled off the side of the road to park in a passing area, said Valais police.
Probably due to snow and ice on the road, during that manoeuvre the vehicle slid off the road and fell 225 metres.
The driver, a 36-year-old man, died at the scene, and his 37-year-old wife soon after her arrival at Sion hospital.
The two children – a girl of 15 and a boy of 11 – were also flown by helicopter to Sion in a serious condition. They were later transferred to the University Hospital of Bern.