Neighbors said a second child may have been in the home, and searchers continued to investigate, Santa Barbara fire Capt. Gary Pitney said.
"The structure was completely destroyed," he said.
The big-rig was hauling two trailers full of gravel when it careened off State Route 154 and slammed into the house on State Street about 6:50 a.m.
The truck's brakes failed, according to a notation on a California Highway Patrol Web site.
The bodies of the man and woman were discovered in the home about 90 minutes after the crash, and the body of the child was found a short time later, Pitney said.
The identities of the victims were not immediately released.
The truck driver was treated for facial cuts, Pitney said.
A vacuum truck was called in to remove some of the gravel that covered portions of the house.
Santa Barbara is about 75 miles north of Los Angeles.