At least eight people, including five police, were injured in the melee, which appeared to be under control by late Friday.
The assailants, who were not believed to be linked to any Jewish nationalist group, were disguised as Christian pilgrims when they entered the Basilica of the Annunciation, police said.
They remained barricaded inside the building for several hours before police broke through a crowd of several thousand angry protesters and took the three away.
A witness who identified herself only by her first name, Rouan, said the church was crowded with worshippers praying for the coming Easter holiday at the time of the blast, which apparently did not cause any major damage.
Police officials said the Jerusalem couple had been treated for psychiatric problems in the past and authorities had questioned them this week and threatened to place their children in foster care.
The officials spoke on condition of anonymity because they were not authorized to speak to the media. No information was available on the woman who was with them.
Israeli Public Security Minister Gideon Ezra said the attack did not appear to have nationalist motivations. He said the husband was Jewish and the wife was Christian. He also said he had been in touch with local Christian leaders to calm the tensions.
The church is at the site where Christians believe the Angel Gabriel appeared before the Virgin Mary and foretold the birth of Jesus.
Nazareth, the boyhood town of Jesus, is located in northern Israel. It is inhabited by Christian and Muslim Arabs and religious tensions have boiled over in the past, with the two sides in a dispute over attempts to build a mosque next to the church.
Now some people claim that people who don't appear to be white but Christian are backwards for some reason.
Here is an example of more Christian violence.