Fairfax reported it is believed they are the last gay couple allowed to use international surrogates to give birth to their children, as Mexico tightens its IVF laws to bring them in line with most other nations.
Today David Beard described the ordeal as "coming out of the closet twice in one life time" on his Facebook page.
The couple desperately wanted to get their children home from Villahermosa, where they said their babies were born in unhygienic hospital conditions.
A plea has been made for help from friends and family, including a social fundraising page, along with a request to the New Zealand and Mexican Governments to cut through red tape and allow the family to travel back home.
Fairfax reported the Mexican Government had assured them they would be allowed to take the children out of the country but New Zealand had told them international surrogacy was a dangerous business with legal risks involved.
International surrogacy by homosexual couples was only recently banned in Mexico, but the Beards said government officials assured them they would be able to take the children home because the surrogates were already pregnant.
Their case has been complicated after the couple allege the Cancun adoption agency took off with all the money they had sent for medical and hospital bills, legal costs and care for the surrogates.
The couple has engaged prominent family lawyer Margaret Casey, QC, to help fight their case.
They are asking for Immigration Minister Michael Woodhouse to intervene, so the three babies could have New Zealand passports issued immediately by the New Zealand Embassy in Mexico City, rather than go through the lengthy process of obtaining Mexican passports.
The Ministry of Social Development's Paula Attrill said the New Zealand Government was aware of the case and had provided advice to the Beards.
