The family of New Zealand soldier Kirifi Mila, killed in an accident while serving in Afghanistan this week, say he was the "Einstein of the family" and will be sorely missed.

Private Mila, 27, also known as Cliff, was standing on the turret of a Humvee, about 8.40pm (NZ time Tuesday) when it rolled down a 30-metre cliff.

Four soldiers were in the vehicle on a patrol which involved three other Humvees.

A private suffered serious head injuries, a sergeant had broken ribs and was now stable, while the other soldier in the vehicle was in shock and recovering.

In a statement released today, Pte Mila's family said he was "much loved son, brother and friend of many" and a "kind, loving and giving person".

His immediate and extended family, who knew him as Lifi or Klyff, would miss him "deeply", the statement said.

He was a great example to all of his family and friends and the family would "treasure the wonderful memories he has instilled in us".

"He took everything as it came and solutions to things often came naturally to him, as he was the Einstein of the family."

"Lifi took pride in his work and was very enthusiastic in learning new things."

"Lifi you always gave all that you had to perfecting every mission right to the very end and this takes courage, determination, discipline and desire."

"We know you are now at ease, 'til we meet again, forever your loving family."

The family also thanked the New Zealand Defence Force for the support they had given him while he was in the army.

Pte Mila's comrades and friends said their goodbyes in a ceremony at KiwiBase in Bamiyan province on Wednesday night.

His body would be flown to Germany overnight and he was expected to arrive in New Zealand mid next week, a New Zealand Defence Force spokesman said today.

Details about his funeral would be made available next week, he said.

One of the soldiers injured in the crash remained at the at Kiwi Base in Bamiyan, while two others had been flown to the United States Military Hospital in Landstuhl, Germany.

The condition of the private, who was admitted to the hospital's intensive care unit, was improving and he was expected to be moved to a ward within the next two days.

The accident happened near the village of Ferosak in the northeast of Bamiyan province, about 30km from where New Zealand Lieutenant Tim O'Donnell was killed by a bomb last year.