Video footage of the latest attack on the police headquarters shows two motorbikes approaching a checkpoint just before the blast. The attack killed the four perpetrators.
Police spokesman Frans Barung Mangera said six civilians and four police officers were wounded in the explosion at the police complex in Surabaya.
In one attack, a family forced their eight-year-old daughter to launch a suicide bombing on Surabaya's police headquarters, according to police.
Experts have warned for several years that when those fighter return, they could pose a significant threat.
Daesh has claimed responsibility for the church bombings.
Oepriarto then drove the van to the Pentecostal Central Church, where, from inside the vehicle, he detonated another bomb, police said. But the fact that children were involved in Sunday's attacks in Surabaya shocked and angered the country.
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Indonesia's president Joko Widodo condemned their action as "barbaric". The top security minister, Wiranto, who uses one name, said the government will attempt to hasten passage of an updated anti-terrorism law that has languished in parliament.
Al-Qaeda has carried out the deadliest attacks in Indonesia, killing more than 200 people on the island of Bali in 2002. Police blamed an Islamic State-inspired network. All six members of the family were killed.
Indonesia has been on high alert for attacks by homegrown militants, including some claimed by ISIS. However, hundreds of Indonesians have flocked in recent years to fight alongside IS there.
Earlier in the day, a couple and a child were killed in their apartment when home-made bombs accidentally exploded in Sidoarjo, about 30km from Surabaya.
At Surabaya Centre Pentecostal Church, Futrianto then drove his auto onto the church grounds and detonated explosives. The newspaper reported that 12 worshippers died in the church attacks.
Police said they arrived after the explosion and shot dead the injured man, Anton Febrianto, as he held a bomb detonator in his hand.