The husband was killed in the accident on Tuesday morning when the balloon touched a power cable as it came in to land and plummeted 50 metres to the ground.
Fribourg cantonal authorities said the mother and her two daughters aged 20 and 24 were still in hospital, the Swiss news service SDA reported.
The pilot was also injured but did not have life-threatening injuries, it said.
The crash victims were tourists from Malibu in California who were staying in Gstaad in the Bernese Oberland.
The husband is reported to have been a descendant of the city’s founders.
The Malibu Times reported that one of the daughters had undergone a successful operation.
The balloon belonged to the five-star Grand Hôtel Park in Gstaad.
The pilot was an "experienced and recognized balloonist", the hotel said in a statement.
The family had taken off from Château d'Oex, which is well known for its annual balloon festival.
Swiss investigators are looking into the cause of the accident. Flying conditions on Tuesday morning are reported to have been good.