Three boys, now aged 7, 6, and 5, were also premature and spent the first three to six months of their lives in hospital.
A fifth child, a girl, was born pre-term and did not survive.
This history explains their distress when the hospital called them on Wednesday to say that a nurse had mistakenly taken Cali from her incubator and handed her to a stranger.
After Mrs Malo rushed to the hospital, the nurse who made the mistake came out to try to explain.
"Her answer was: 'I was just too busy, I just gave her the baby'," Mr Mola said. "She gave our daughter to a stranger, she didn't check the ID bracelet on her ankle, the ID tag on her incubator, didn't check reports."
An investigation is being made, and to reassure the family, swabs have been taken to check for problems, although staff do not expect any medical consequences to arise from the incident.
Mr Malo, a 30-year-old supervisor for a mobile recycling facility, said he and his wife had since learned that the woman who held Cali was a first-time mother who had not properly seen her own baby since a late-night delivery.
"That was the first time that she'd seen the baby. So she had physical contact and a bonding experience with our daughter.
"And then being told 15 minutes later, 'We're sorry, this isn't your child'. My wife and I can feel for this woman, having that told to her."
The Malos would now like to meet her.
"She has made a bond and connection that I've been waiting for for the last two months," Mr Malo said.
"I mean, a complete stranger to hold your child before you? Yeah, it's upsetting."
Waitemata DHB's head of medicine for child, women and family services, Dr Tim Jelleyman, said the hospital had unreservedly apologised for the mistake.
It was extremely unusual and went against protocol, including checking of a baby's ID bracelet.
"To reassure the Malo family and as a precautionary measure, swabs have been taken to ensure that baby Cali has not - on the very slim chance - picked up any infections through this brief period.
"Cali is doing well and appears unaffected by the incident. We expect no medical consequences to occur. Our main concern is for the distress this event has caused the families and to support them through this period."
Mr Malo said he wanted to speak out to make sure the same thing did not happen to other parents.
"They are caring for our daughter in there who needs support, and they've broken the trust ... no one knows how an infection affects a child, and there is no timeframe on what the effect is."
