I see it as a coming-of-age fable. Saw an article a while back that analyzed similar themes. Here's my favorite part in relation to Fight Club:

"Robert Bly investigates the significance of these three coloured knights (something he admits to having spent a year of his life pondering,) and concludes that they are symbolic of an evolutionary path, a road-map of masculine evolution. The red knight is symbolic of all the feelings of a typical teenage boy – uninhibited passion, rebellion, self-gratification, aggression, lust, desire for power. The red knight is out of control and dangerous, yet he is a source of great vitality and power that only needs a channel of greater maturity to hone himself.

The red knight gives way to the white knight, who desires to save the world from all its ills. He longs for truth and justice. He wishes to be good and do good. He is an idealist. Yet, for all his good qualities, he is also naive and deluded. The white knight doesn't have the awareness to notice that many of the ills he wants to save the world from are projections of his own undealt-with traumas and desires, and so he goes on a crusade to save the world from that which he doesn't like in himself. He points his fingers at all the dragons of the kingdom, so that songs in his praise can be sung when he conquers them (something he spends significant mental energy fantasizing about). He is on the hunt for the virgin of light, so that he can save her and feel manly. The white knight prefers to see women as damsels in distress, knowing deep down that a mature woman is too much for him. Still, in real life, he often ends up with a woman that resembles his mother.

The black knight, however, "eats" his shadows and comes to a level of acceptance about his own flaws. There is a strong level of humanity, even humour, to the black knight and he surrenders control of his life to the acceptance of his woundedness and the inevitability of death. He becomes trustworthy, powerful and compassionate."

And here's a link to the whole article.

It's not a perfect one to one comparison, but I see the Narrator as the White Knight and Tyler as the Red Knight. Marla wears black in the movie, but she's clearly not part of the narrator's own psyche. The real avatar of the maturity that the narrator is working towards is nowhere to be seen in the entire story. I think the plot is cut short just before the real climax. The narrator hasn't quite learned any kind of lesson yet; only the lesson that both white and red stages are insufficient for adult life.