The couples, all from Utah, were members of Church of Jesus Christ of Latter-Day Saints and were on their way to the Mormon temple on the outskirts of Hamilton when the crash happened.
Mr Peterson was an optometrist who owned a practice in Richfield, Utah. He was also a bishop within the Mormon church.
He and Mrs Peterson are survived by five children - two daughters and three sons, with the youngest aged just 8.
In a family statement they were described as a couple who loved being involved in the community.
"They constantly served others through their church callings, as well as through community involvement, and did their best to bring joy to those around them."
Dr Barnett is an orthodontist who practises in Richfield and also serves on the city council there. He and Mrs Barnett have four children and four grandchildren.
A fundraising page has been set up to help Dr Barnett and his children take their wife and mother home for her funeral.
"Our dearest wife, mother, daughter, sister, aunt, grandmother and friend Tammy tragically left us while on the trip of a lifetime to New Zealand with her beloved husband Richard," a family spokesperson said on the page.
"Tammy had an incredible energy about her and will be sorely missed."
Dr Barnett were being supported by the Hamilton branch of the Church of Jesus Christ of Latter-Day Saints.
"We convey our deepest sympathies to family members and friends of those who have lost their lives, and will support them as they mourn the loss of loved ones," said Pacific area spokesman Richard Hunter.
Waikato Inspector Jeff Penno said initial indications are that the couples' rental vehicle, driven by Dr Barnett, turned right across the path of a southbound truck and trailer unit.
The crash happened at the intersection with Tuhikaramea Rd - where the Mormon temple is located.
Mr Penno said an off-duty policeman on his way home was the first person to come across the crash.
