Read the full HDC report online here
The Barlows have a 7-year-old son, Orry, and another son, Flynn, who turns 2 in May and was born through a surrogate mother and in vitro fertilisation.
Mrs Barlow told the Herald the couple received the written apology yesterday, more than four years after Adam died, but said it was too personal to comment on.
However she said they hoped proceedings against Ms Rowan would go ahead to ensure the mistakes were never repeated.
"We've gone through this for 4 years to find answers," Mrs Barlow said. "We want the maternity system, the midwifery system and families to all learn from what happened to me, Adam and our family and that systems are put in place to improve maternity services so that it's much safer for people in New Zealand."
Waikato District Health Board has also apologised after the Waikato Hospital obstetric registrar was criticised for failing to adequately assess Mrs Barlow and for instigating an inappropriate treatment plan.
Mr Hill also found Mrs Barlow received poor midwifery care from the public hospital midwives.
The Barlows called the horrific labour and their son's death a harrowing and preventable experience.
They blamed the inexperience of Ms Rowan, who had been a midwife for seven months at the time, as a major factor in their son's death.
Mr Hill found eight failures by Ms Rowan including that she ignored River Ridge birthing centre policies requiring specific heart monitoring of the patient before and after administering the controlled drug pethidine.
She sent Mrs Barlow home without further assessment and against her wishes and failed to adequately monitor the fetal heart rate or transfer Mrs Barlow to hospital in time. When Mrs Barlow arrived at Waikato Hospital she suffered a ruptured uterus and stopped breathing after having an epidural. She had an emergency caesarean but was bleeding profusely internally and had to have an emergency hysterectomy.
Then 31, Mrs Barlow suffered a heart attack on the operating table before being taken to intensive care on life support, not knowing that her little boy had died.
Health Waikato chief operating officer Jan Adams said the DHB had already made several changes because of the case.
Ms Rowan did not return Herald calls.