The father, 43, who on Wednesday pleaded guilty to three charges over the little's boy death in August 2012, told police he, his wife and their two sons formed a "good little family unit", documents tendered to Melbourne Magistrates Court say.

"We loved our children - we love our children," the man told police in an interview in March last year.

"We - in our eyes did everything - we ... [were] such a good little family unit. And, OK, we weren't perfect, but who is? And we tried our best.

"And, you know, it was never a case of not loving him and I tried to provide for them."

The five-year-old boy died days after cutting his big toe on his left foot an open can of cat food that was discarded in the house and was piled among junk, food scraps and other filth in the family's home, according to court documents. The house is in Melbourne's north-western suburbs.

The boy suffered a three-centimetre cut when he stepped on the can, the documents say, and after falling ill in the following days, he was discovered lifeless in his bedroom by his mother on August 1, 2012.

He was taken to an ambulance branch office but could not be revived by paramedics.

The boy's father on Wednesday pleaded guilty to two charges of reckless conduct endangering serious injury and one count of failing to register the birth of a child.

The man's 41-year-old wife, the mother of the boy, pleaded guilty to the same charges two weeks ago.

The names of the couple and their son have been suppressed to protect the identity of the couple's other son, who was eight at the time of his brother's death.

In an interview with police in March last year, the boy's father said he and his wife were having nightmares and that he felt he had let his son down.

But he told police he did not feel responsible for the boy's death, nor did he hold his wife responsible. He declined to answer when asked who should be held responsible.

In the interview, the man said he worked long days in his role as the financial provider for the family, while it was his wife's task to raise and school the two boys.

In a separate statement given to police, made on the day the boy died, the father said his wife was a "magnificent mother", who would "cut her left arm off for the boys".

He said she spoilt them "rotten" and had showed a lot of patience with them.

In an interview with police in March last year, the boys' mother admitted she was embarrassed and ashamed about the filthy state of the family's house, but had been "overwhelmed" when it came to trying to clean up the mess.

The court has heard toxicology reports have been unable to determine how the boy died.

Statements given to police say tetanus could have been a cause, botulism could not be excluded and food poisoning was possible. Other statements say E.coli was detected on the boy's toe, under a dirty bandage.

Court documents show police visited the family's house at least twice before the boy died, following complaints by neighbours, and child-protection workers were also informed over concerns for the safety of the two boys.

The boy who died was born at home, was never immunised or enrolled in school or kindergarten and only really had contact with his immediate family members, court documents say.

His parents said in statements he rarely got sick and so never went to a doctor.

The boy's death and the state of the house he was living in has shocked police and court officials, and prompted an investigation by Bernie Geary, the principal commissioner of the Commission for Children and Young People.

Details about the case were also conveyed to the office of Community Services Minister Mary Wooldridge. The State Coroner is expected to investigate later this year.

The boy's parents are on bail and due to appear before the County Court on June 2.