A Newtown, Conn., family rocked by the Sandy Hook school-shooting massacre is now reeling from a fire that destroyed their home.

Hans Barth, his wife, Audra, and their three children lost everything in the Wednesday afternoon blaze, including their 5-year-old Chihuahua, Goliath, and several baby chickens.

“This is the icing on the cake,” Hans said yesterday as he surveyed the house’s charred remains.

The Barths’ children — including 7-year-old Peter Barth, who survived the massacre with his classmates in a locked school bathroom — were “pretty shaken” by the blaze, Hans said. Peter was in the classroom of teacher Kaitlin Roig, who heroically barricaded her students during the attack.

Hans Barth said he and his wife hope to move their family into a bank-owned house that’s next door to their destroyed home. For now, the family is living in a motel.

Whatever happens, the Barths plan to stay in the neighborhood.

“Our kids have been through a lot. To tear them out of their home now it would be the worst thing we could do,” Audra Barth said.

Peter’s sister Shanice, 8, was a Sandy Hook third-grader. The couple also has a 2-year-old son, Jacob.