First, that people should try to think about moral questions on their own. This stands in opposition to authoritarianism, which says that people should just blindly follow the moral code dictated to them by their betters.
Second, that moral questions should be resolved by thinking about the well-being of all of humanity. This is in opposition to tribalism, which says that you should only think about the well-being of your particular culture or sub-culture, and ignore the consequences to outsiders.
These are derived from the basic human characteristics of rationality and empathy, so they pre-date written history. (Even atheists have empathy, which I think should answer the questions you had about why an atheist would want her children to be happy.) In Western Civilization, the various Greek philosophers made the first recorded attempts to formalize these ideas.
During the conquests of Alexander the Great, their writings got spread around Asia Minor and the Levant and merged with Archaic Judaism to form a bunch of philosophical systems, including proto-Christianity. The "Parable of the Good Samaritan" is one of the best early statements of the two Humanist ideals.
During the reign of the Roman Emperor Constantine, Christianity was adopted as the state religion, and was reinterpreted to fulfill the Authoritarian/Tribalist needs of the Empire. The Humanist elements were discarded, leading to the Dark Ages; a thousand years of heresy hunts and witch burnings and all-around bloody mayhem.
This isn't to say that all modern Christians are Humanists. Some are - Dr. Martin Luther King is the first example that comes to mind. But there's also a strong anti-Humanist faction; Fred Phelps is one of the noisier adherents of this world-view.
All that said, Humanists are prone to the usual range of human failings. If a Humanist does something wrong, and you tell him, "You know, you're being a real jerk!" then it's certainly possible that he'll come up with some kind of lame rationalization for his behavior. On the other hand, you don't have to worry about him saying, "God ordered me to be a jerk!" as if that were an excuse for anything.