Story highlights Police identify the suspected gunman as 55-year-old Desmond John Moses

A mother runs from the house carrying her youngest child though she's shot in both legs

The 4-year-old boy, shot in the head, later dies in surgery

The father died after using his body as a shield over his other children

A father and mother showed heroism when a gunman opened fired inside their California home before dawn Saturday, but two members of the family couldn't overcome their wounds, Inglewood police said.

The mother ran from the house carrying her youngest child, though she was shot in both legs, in an "extraordinary rescue attempt," police said. The 4-year-old boy, however, was shot in the head and later died in surgery. The mother was in critical but stable condition Saturday afternoon.

Inside the house, the father used his body as a shield in trying to protect the other three children.

Despite the father's efforts, the gunfire wounded two of his children: a 6-year-old boy in the pelvis and a 7-year-old girl in the chest. Both were in critical but stable condition, police said. The father later died in surgery of multiple gunshot wounds.

The oldest of four children, an 8-year-old boy, was the sole family member who wasn't injured, police said.

Desmond Moses is suspected in the shooting of a couple and their children.

"What would motivate an individual to do this is inexplicable," Inglewood Police Chief Mark Fronterotta said. Inglewood is adjacent to Los Angeles and its international airport.

Police were conducting a manhunt for the suspect, who lived in a house in the rear of the property. That rear house was also set afire, believed to have been ignited by the gunman, police said.

Police did not release names of the father, 30; mother, 28; or their children as of Saturday afternoon.

The incident occurred about 4 a.m. Saturday when police received a report of 10 gunshots at the property. The fire department also received a call at the same time.

Firefighters were hampered by fears that the gunman might have been armed in the rear residence, police said. Fallen power lines also hindered firefighting efforts.

The suspect was described as a 55-year-old black man with a dark baseball cap and is 5-foot-6 and 160 pounds, police said. They later identified him as Desmond John Moses.

The suspect wore a painter's mask when he gunned down the family, the police chief said.

Police didn't provide a motive.

The suspect should be considered armed and dangerous, the police chief said.