"Schulz and Peanuts" by David Michaelis portrays the cartoonist as complicated, humble and melancholy, the newspaper said.
Michaelis spent seven years researching the book and had the cooperation of his family.
But two of Schulz's five children said the book doesn't convey Schulz's role as loving father, portraying him instead as a figure more distant than supportive. Monte Schulz said the book also dwells on the negative and misreports facts.
Charles Schulz's daughter, Amy Johnson, told USA Today: "We were all very deceived. We never should have allowed (Michaelis) into our homes."
However, Michaelis contended he "invited any corrections for any mistakes" and emphasized the book depicts Schulz as a "great artist."
"It is not debunking him or taking him down a peg," he told the newspaper.
The book said Schulz's life and personality were reflected in his beloved characters.
Michaelis said Schulz gave "his wishy-washiness and determination to Charlie Brown … to Lucy his sarcasm, to Linus his dignity and 'weird little thoughts,'" the USA Today report said.