BANDUNG, Indonesia — One suicide bomber appeared to have been disguised as a churchgoer. Another drove a Toyota minivan with a bomb to one attack site. Still another was seen in footage speeding on a scooter toward a church before an explosion.

After the back-to-back bombings that targeted three churches in Surabaya, Indonesia’s second-largest city, as worshipers gathered between services on Sunday morning, the police said they had been the work of one family: a couple who had led their four children on a terror spree that took their own lives and those of at least seven other people.

The Islamic State claimed responsibility for the attacks, according to the group’s news agency, Amaq. In an initial bulletin, the group described each of the bombings as a “martyrdom” operation. In a subsequent, longer media release, the Islamic State identified three modes of attack: a car bomb, a suicide vest and a motorcycle-borne bomb.

