All members of the family died in the attacks, which ISIS claimed responsibility for via its Amaq News Agency in what it called "a martyrdom operation".
The coordinated attacks killed 18 people, including the bombers, and injured more than 40. Jemaah Islamiyah, the al-Qaida affiliated network responsible for the Bali attacks, was obliterated by a sustained crackdown on militants by Indonesia's counterterrorism police with USA and Australian support.
Three attacks, including one suicide bombing, were carried out in Surabaya early today.
Separately on Sunday, three members of another family were killed when homemade bombs exploded at an apartment in Sidoarjo, a town bordering Surabaya, police say.
The bombs were detonated within minutes of one another, at around 7:30 a.m. local time, on Sunday, May 13, just as people were arriving at the churches for morning services, according to The Jakarta Post. Police killed the men after they had produced weapons during the raid and evidence confiscated included revolvers, bullets and an arrow with a bomb placed on the end of it, Wasisto said. "This is one family", he added.
Karnavian identified the father as Dita Futrianto and said he was head of the Surabaya cell of Jemaah Anshorut Daulah, an Indonesian militant network affiliated with IS that has been implicated in attacks in Indonesia in the past year.
Hay tres detenidos por homicidio de estudiantes de cine, falta uno — Segob
Al momento se han concretado tres de órdenes de aprehensión de las cuatro que fueron emitidas, informó la Agencia Notimex. Según la narrativa de la Fiscalía, el joven murió a causa de los golpes y por ello asesinaron a sus dos compañeros.
Indonesia is home to the world's largest Muslim population, the majority of whom practice a moderate Islam.
The girl was with two other adult attackers on a motorcycle and was thrown out of the moving vehicle but survived, police spokesman Frans Barung Mangera said.
"Because their leaders are detained, their groups could be retaliating", said Karnavian.
Indonesian President Joko Widodo condemned the attacks as "cowardly, undignified and inhumane" and pledged to push through the national legislature an anti-terrorism bill should the parliament fail to pass it. Indonesia was on high alert after bombings on Sunday by a single family targeted three churches in Surabaya, the capital of East Java province.
Indonesia has seen resurgence in violence in recent years after hundreds of people left for Syria and Iraq to join ISIL, also known as ISIS.
"(The Secretary General) reiterates the support of the United Nations to the Government and people of Indonesia in their efforts to fight and prevent terrorism and violent extremism, including through the promotion of pluralism, moderation and tolerance", the statement said.