"The things I have learned about a baby's digestive system is incredible."
Scattered around the lounge and kitchen of Ardern's house was the usual paraphernalia of a newborn baby - flannels, beanies, breast pumps and bottles.
Gayford will be taking on the role of primary caregiver while Ardern is working and Ardern said he had started off well, taking on the lion's share of nappy changes.
"And he's very good at settling her, which is helpful."
She had had one memorable nappy change of her own. Asked if anything had happened that resulted in hysterical laughter, she said "the poonami."
"It is just as it sounds. Everything coming at once. It was me who was changing her at the time."
She was coping with the interrupted sleep, partly because she and Clarke had been sharing the load and the two grandmothers were also chipping in.
"It's disrupted sleep, but still I've always had friends and family saying it's different when it's your own. Getting up in the night for your own little one is not as hard."
Ardern formally took back the reins as Prime Minister from Deputy Prime Minister Winston Peters at midnight on Wednesday night and will move into Premier House with Gayford and Neve on Saturday. On Monday she will be back at Parliament.
She said she did have mixed feelings about returning to work but had not been tempted to give it all away.
She had not gone through the dilemma many parents faced of whether she would return to work, because there was only one answer.
"So I've know that's something that's always been on the horizon, that I will have to walk out the door. So I've just gotten used to that idea."
She was expecting to feel some guilt about dividing her time. "I understand how acute it will feel. But I think lots of parents feel guilt that either they're not doing enough in their parenting role, or they're not doing enough in their nine-to-five role.
"There is guilt behind every door. I am definitely aware of that. We can't do everything. The best we can do is make the best of it."
Ardern has what she will need for Neve to spend time in her office as well as at Premier House.
While babies can now be taken into the Debating Chamber with their parents, Ardern did not believe that would be necessary given she did not spend much time there other than at Question Time.
"There might be times when I might, but by and large I don't think I'll have to which will be very upsetting for the Speaker."
She did not intend to take Neve in just to make a statement. "No. We have MPs who have a very legitimate need already to have the children in the Debating Chamber, and they have. I don't think that should be something we have to make statements about. It should just be a natural thing."
Ardern is clearly keen to keep Neve as private as possible. Media were not allowed to take photographs during the interviews and instead the Prime Minister's office provided photos later - in all of which Neve's face was obscured.
Parliament's Speaker Trevor Mallard has also set out new rules for filming and photography on Parliament's grounds to ensure Neve will not be filmed while on the grounds - the penalty for a breach is for journalists to be stripped of their accreditation to cover Parliament.
