The group is putting ads in newspapers across the country - and advertising on NBC - in the $200,000 campaign, AHA head Roy Speckhardt told CNN.
The point, he said, it to "challenge the fundamentalists" who "spout their backward ideas," he said.
The target audience is people who may not realize they are humanists, Speckhardt explained.
"We're targeting for criticism those who read the Bible literally, not those who pick and choose what they like," he said. "We're telling (people who pick and choose), 'You're more like us.' Biblical literalists and Quranic literalists are holding us back.
"We know that you can be good without God, but many folks in America don't know that," he said.
The campaign features violent or sexist quotes from holy books, contrasted with more compassionate quotes from humanist thinkers, including physicist Albert Einstein.
"We're calling it like it is," Speckhardt said. "It's quite obvious that the Bible contains horrific material - and the Quran - and to say you get your morality from there" is problematic.
"We don't expect to convert people from the billboard signs," he said.
But, he said, "there are millions of people - approximately 34 million people - who are unaffiliated" with a religion in the United States.
Only one in 20 Americans does not believe in God, according to the Pew Forum on Religion & Public Life, and of that group, only a quarter call themselves atheists. The rest say they are agnostic, "nothing in particular" or members of a faith.
More than half of all Americans pray every single day - as do more than one in five Americans who say they're not affiliated with a religion, according to Pew's U.S. Religious Landscape Survey.
Speckhardt knows the numbers.
"There has only been one member of Congress in the history of the United States who has come out and said he doesn't believe in God," Speckhardt said, identifying the legislator as Rep. Pete Stark, D-California.
The Secular Coalition for America said Stark responded in 2007 to an inquiry from that group by saying he was a "nontheist."
"We feel those (unaffiliated) folks don't yet know they can admit that they don't believe in God," Speckhardt said.
Marketing guru Allysen Stewart-Allen thinks the campaign has potential.
"They will certainly get people talking," she said.
"One of the things that the humanists need to articulate is what success looks like for the campaign - if it's converts, I wouldn't think that is a realistic measure," said Stewart-Allen, the director of International Marketing Partners.
"I would hope what they want is for people to talk about faith in the widest sense, and I think they will achieve that," she said.
"If your objective is to shape the conversation, I think it can't hurt," she added.