It's unfortunate, I think, that we so often use the word "faith" as a synonym for "belief". The two are very different things. Belief is a matter of taking a position on the truth value of a statement, whereas faith is a matter of acting as if something is true, without necessarily believing that it is.
In large part, it was law school that brought me to an understanding of faith, as distinct from belief. As they drill into us, "Nobody cares what you think." That's most commonly heard when preparing for a moot, when many students fall into the speech habit of saying, "I think that..." which generally speaking just isn't good rhetorical technique (though in some cases it can be very effective), but in fact it really does go to the core of legal ethics.
Consider representing a defendant in a criminal case. You might well believe your client to be guilty. Heck, you might believe this so strongly that you'd say you know he's guilty. But nobody cares what you think (or what you think you know); your job is to give your client the best representation possible, to ensure the integrity of the legal process. You need to put aside what you think, and present to the court the best evidence and argument (subject to the proviso that you must do so with scrupulous honesty) for your client's case, and have faith that the judge (and jury, if any) will come to the proper conclusions on their own.
Now, you may not actually believe that the prosecutor will present enough evidence to convict your guilty client, and you may not believe that the judge and jury are actually smart enough to reach an appropriate verdict and sentence, but that is not your call to make. You are not the one charged with the responsibility of deciding your client's guilt or innocence, and your own prejudices could easily undermine the whole process if you attempt to preempt the court's judgment with your own. In order for the system to work, you must do your job, and leave it to the prosecutor, the bench and the jury to do theirs. So you must make your arguments with the available evidence as if you believe your client to be innocent, whether you do or not, and as if you believe your counterparts in the process are competent, whether you believe it or not. In short, you must act in good faith, regardless of what you believe.
Contrast this notion of faith with religion's emphasis on belief. Many religious people go well beyond claiming to believe that God exists; they claim to know so. It is as if the fervency of belief is a measure of piety; the more certain one feels, the fewer doubts one harbours, the greater the devotion.
As a philosopher sharing in Descartes' radical skepticism, I find this concern with belief to be baffling. How can we puny, fallible mortal sinners possibly lay any claim to infallible certainty about any fact? It seems to me obvious that we are all capable of error, and indeed all churches seem to try to point that out: there may be a God, but we are not it. So the focus on certainty of belief itself strikes me as fundamentally impious right from the start.
Yet faith is something else entirely, and does not demand that we overcome our human epistemological limits. All we must do demonstrate faith is to act as if we accept a proposition as true. We are free to doubt that it is true, and indeed I think that people of honest intellect are morally obliged to acknowledge doubts.
That is why I don't object to describing myself as an atheist of faith, when I bother to describe my (lack of) belief at all. (I have also occasionally referred to myself as a Zen Catholic. A koan: What happens when you give up religion for Lent?) I have infinite faith in God's goodness, and none in His existence. This means that while I don't actually believe God exists, and more frighteningly, while I have no evidence whatsoever to suggest that if He does exist He's not an evil spiteful monster, I simply have to act as if I believe that a truly omniscient and omnibenevolent God will have perfect knowledge of my reasons and motives, and will not condemn me to the unspeakably nasty afterlife many religions threaten sinners and unbelievers with.
These threats, by the way, lead to a curious paradox: many of those who believe (or who profess to believe) do so in bad faith: they do not trust God to be perfectly just and merciful, and thinking they err on the side of caution (consider Pascal's Wager), they go along with whatever their church, synagogue, temple, mosque or religious leader commands, perhaps expecting the "I was just following orders!" defense to be a complete answer. Me, I doubt, but I do so in good faith and with a clear conscience. At least, as clear as the conscience of one who knows himself to be fallible can be.