They say he would have died if they, their midwife or the hospital had not acted so quickly.
"They [doctors] said it's a very weird condition - it's not something they see very often and usually they wouldn't make it. It is a bit of a miracle he's around us really," Ms Diaz said.
Between one in 5000 to one in 9000 babies worldwide are born with fetal maternal haemorrhage and there is a high mortality rate.
The condition, also known as "ghost baby" due to the pale colour with which they are born, can be deadly because of the loss of red blood cells which transport oxygen.
Baby Tane was given a blood transfusion minutes after he was born and needed two more the days following. Over the next few days his skin colour started transforming from a pale white to a healthy pink glow.
Ms Diaz, who is originally from Argentina, thought she was going into labour two weeks early when she felt her baby bouncing around inside her.
A few hours later on the Saturday evening the movements suddenly stopped and she couldn't feel the baby at all. Her pregnancy had been going smoothly until then and the first-time parents initially thought the baby had just run out of room.
But the 31-year-old restaurant manager kept prodding her stomach over the weekend to make the baby move and by Monday morning she called her midwife as she was worried. A CTG scan showed the baby's heart was beating more slowly than it should have been and by 11am the same morning, Ms Diaz and Mr Anselmi had been checked into Auckland City Hospital. They had travelled to Auckland from their Waiheke Island home by ferry.
"At this stage we didn't know how bad it was or how urgent it was because the CTG wasn't that clear something was really wrong," Ms Diaz said.
Doctors reacted quickly as Tane's heart rated started to drop and by 1.15pm that afternoon their baby was born by an emergency caesarean section, weighing 2.890kgs.
"When they took him out he did like a little cry, and I thought 'he's alive, oh good'." But it wasn't until an hour later after Tane had an urgent blood transfusion and Ms Diaz had recovered from her own surgery that she got to see her son for the first time.
Her husband had been with him since about 10 minutes after he was born and had been careful not to worry her about their son's pale colour or heavy breathing as she recovered from her operation.
"They took me with the bed to see him in NICU. And he was all with tubes and cables everywhere. It was really scary," she said.
After six days in NICU, Tane was shifted into a ward with his mum and had made such a speedy recovery that a week after he was born they took him home. Ms Diaz said he had settled in well and was "excellent". He was feeding and growing well and becoming more alert.
Auckland City Hospital neonatologist Dr Kitty Bach said fetal maternal haemorrhage was relatively uncommon and could be fatal if not treated quickly. . The cause was unknown.
Dr Bach said it was important the condition be picked up quickly and urged mums-to-be to contact their midwives or lead maternity carer if they noticed their baby's movements decreased.
