The family that carried out three church bombings in Indonesia's second-biggest city on Sunday were just "ordinary" people, according to their neighbours.

Key points: Six people from one family responsible for attacks

Six people from one family responsible for attacks At least 14 killed and dozens injured

At least 14 killed and dozens injured Joko Widodo describes attacks as "barbaric and inhumane"

Six people from the one family, including an eight-year-old girl, blew themselves up in coordinated suicide attacks, which left 14 dead and dozens more injured.

Their father, 46-year-old Dita Oepriarto, dropped his wife, 42-year-old Puji Kuswati, and two girls aged 12 and 8 to one church, before driving a car packed with explosives to another, and blowing it up.

Sorry, this video has expired At least 13 people were killed and dozens injured in what police say is one of the worst attacks on the Christian minority.

At another church across town, the couple's two sons, aged 17 and 15, rode an explosive-laden motor scooter into a crowd and set it off.

The neighbours of the family are in shock at the news Oepriarto, Kuswati, and their four children carried out the attack, saying there were no warning signs of what they were about to do.

42-year-old Puji Kuswati poses with her four children. ( Supplied )

What they described to the ABC was a family they regarded as very normal, recalling how the children played with their own kids in the street, and how they rode bicycles together regularly.

"Mr Dita was kind. Familiar to his neighbours. Socially active. An ordinary person living in a normal neighbourhood," neighbour Binawan Widiarto told the ABC.

"His children often played in front of our house. Playing soccer, riding bikes. Picking flowers."

The neighbours say there were no warning signs of the attack. ( ABC News: David Lipson )

Photos the family posted on Facebook also appear to portray typical domestic life, showing them on white-water rafting holidays in North Sumatra and strolling through mangrove forests.

"I'd known him for a long time and the last time we met there was nothing different at all," Samsul Hadi, another neighbour of the family, told the ABC.

"No awkward body language. Nothing hurried."

Despite initial reports that the family had been to Syria, neighbours who profess to have known them for a decade said they had not.

The father, they recalled, spent the night before the attack on the porch, making plans for the Ramadan holiday.

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Widodo: Attack was barbaric and inhumane

Indonesian President Joko Widodo ordered a full investigation into the roots of the organisation blamed for the three church bombings.

Mr Widodo toured the bomb sites, describing the act as "barbaric and inhumane".

"I ask all people to join together in the fight against terrorism and radicalism," he said.

"It's against our religious values, the precious values of God and diversity.

"No words can describe how deep our condolences are for the fallen victims."

Security has been stepped up at churches across Indonesia. ( ABC News: David Lipson )

The Jemaah Ansharuut Daulah (JAD) network, a group of Indonesian radicals, which has pledged allegiance to the Islamic State (IS) group, is thought to be behind the attack.

Police believe the suicide bombing father Oepriarto was the head of JAD in East Java.

Police originally believed he and his family recently returned from Syria, but later confirmed that they had not travelled to Syria to fight for Islamic State.

Five hundred Indonesians are believed to have returned home since the routing of IS forces in Syria.

Police say sleeper cells across Indonesia have woken up in the days before Ramadan.

Last week, terrorist inmates at a Jakarta prison killed five elite police, while on Saturday police shot four terrorist suspects in West Java.

Armed guards are now patrolling churches and places of interest across the country, fearing more attacks in coming days.