"Blonde Ambition: The Untold Story Behind Anna Nicole Smith's Death," by journalist Rita Cosby, hit stores Tuesday.
Birkhead, the father of Smith's infant daughter, said that though he has yet to see the book, he intends to sue Cosby, her sources and Grand Central Publishing.
"This is going to be one of the most expensive lawsuit settlements in book-publishing history," Birkhead told The Associated Press on Tuesday.
Stern also planned to "file and aggressively pursue a libel case" against Cosby and her publishers, his attorney, L. Lin Wood, said Tuesday.
Birkhead acknowledged meeting with Cosby several times after Smith's death in February. But he flatly denied that he and Stern, Smith's attorney and sometime boyfriend, ever shared a sexual tryst.
"It's totally false and defamatory," Birkhead said. "This book is fueled by Internet gossip and tabloid reports. She never once tried to contact me or Howard to see if any of these things were true."
Cosby quotes Birkhead on some topics in the book, she said, but not on the sexual rumors.
"We also knew what Birkhead would say because we've seen him inconsistent on many other things," she told AP Tuesday, adding that the book cites numerous sources and was "carefully vetted through attorneys at our publishing house."
Birkhead denied the book's claim that he and Stern made a "secret deal" about finances and the custody of Smith's daughter, Dannielynn.
"There's been no deal cut. There's nobody even positioned to make deals," Birkhead said, noting that he is still involved in a custody dispute with Smith's mother, Virgie Arthur.
Cosby said she expected backlash from Birkhead and Stern when she started writing the book in April.
"I knew going into this that this was going to be challenged by them at every turn because they don't want the truth to come out," she said.
Birkhead said the sources Cosby cites "all have pending litigation against me so they all have axes to grind."
He also accused the author of opportunistic timing: "Rita Cosby uses this week, the week that my daughter turns 1 and the anniversary of (Smith's son) Daniel's death, to try to sell a book or two."
Cosby said Dannielynn inspired her to write the book.
"The real issue here, and the reason I did this book, was that little baby," she said. "The question is: What's ahead for her future if these two men appear to be in collusion? ... I hope that my book will expose some of the inconsistencies that have been out there and maybe have these cases given a second look."
Dannielynn turns 1 on Friday.
Grand Central Publishing did not return messages seeking comment.
By Sandy Cohen