"She had the baby on Monday morning and it was 2.30 on Wednesday morning before she died. She was walking around happy as hell.
"It's really hard. We are still struggling to come to terms with it."
Health authorities say only 10 New Zealand women on average die each year from pregnancy- and childbirth-related causes.
But Mr Pepperell said Claire's death was so hard to understand because she had seemed so well after Cameron arrived.
"It was nearly two days after the birth so we are not sure what even happened at this stage and they don't know what happened. It's all under investigation ... "
Ms Pepperell's younger sister, Tracy, said the family were waiting for "definite answers".
"Claire was the best sister I could have ever asked for. We are all doing the best that we can at this difficult time. Everything is still very much up in the air."
Ms Pepperell's partner, Brad Wakelin, tightknit family and a large number of friends gathered at the Tauranga Yacht and Powerboat Club on Tuesday for her funeral. "They gave a wonderful tribute to her," said a relative.
A review is under way at Tauranga Hospital after the mysterious death on November 25.
Bay of Plenty District Health Board general manager of governance and quality, Gail Bingham, said Ms Pepperell's death had been referred to the coroner.
"The DHB cannot comment other than to say that it has also initiated its own review of this unfortunate death.
"Investigations are undertaken into all unexpected deaths and/or those which are subject to a coroner's inquiry."
According to the Health Quality and Safety Commission, which compiles annual reports on perinatal and maternal mortality, about 10 New Zealanders die each year as a result of pregnancy or childbirth complications.
In 2013 - the last year for which a report was published - 12 mothers died during pregnancy or in the first six weeks after giving birth.
A spokeswoman for the Action to Improve Maternity support group, Jenn Hooper, said maternal deaths could be linked directly or indirectly to childbirth.
"One of the first things you think of is, 'How did the birth go? Did she haemorrhage lots? Was there an infection? Was there any kind of aneurysm thing that might have happened?"
A friend of the Pepperells said the death was not the first tragedy to befall them - Mr Pepperell's mother, Karina, died suddenly in 2003.
"When I saw that this happened with Claire, I was absolutely shocked and horrified to think that this family were coping with another terrible, sudden tragedy," said the friend, who did not wish to be named.
"They are a lovely family and I just feel completely stunned to think that this has happened again for her dad and for Tracy, and of course for her partner and their baby."
Online tributes have also been paid to Ms Pepperell.
"Such a beautiful young woman," said Elaine Troop. "At times like this it is hard to make sense of life."
Janine Bould said: "I am as shocked as everyone and I will find it hard when I visit ... and Claire isn't there to great me as she did quite often."
