I don't consider Nihilism and Absurdism to be mutually exclusive:
My Existential Crisis is Nihilistic in nature; specifically, I am alarmed and devastated by the fact that my life and existence have no objective purpose, meaning, or intrinsic value.
In the face of such an Existential Crisis, there are three classical coping methods:
1) Suicide - While it is appealing to end the despair immediately, I do not choose this option because I understand that I have the capacity for pleasure, so I might as well experience as much as I can before I die.
2) Religion - While it is appealing to have all the "truths" of the universe told to you, plus a higher purpose for your actions and an eternally blissful afterlife to boot, I do not choose this option because I am rational, so I only accept logical evidence as valid, and I see faith-based evidence as invalid. Basically, I would love to be religious but Scientific Positivism makes too much sense.
3) Absurdism - The final method is to BE A BADASS and laugh in the face of the existential crisis: if there is no greater purpose or meaning, then I am bound by nothing, so I can do whatever I want! I can rejoice in doing absurd things, and sometimes even successfully delude myself into thinking I have Free Will! Some people say that there is no real distinction between Religion and Absurdism.
Nietzsche understood these options and coined the terms "Passive Nihilism" and "Active Nihilism". An example Passive Nihilist is someone who gives up in the face of an existential crisis; the term has wimpy connotations. Nietzsche writes that Christianity is an example of Passive Nihilism (Christians accept the meek, and have a generally self-deprecating and inferiority-ridden mentality.). An Active Nihilist is someone who strives to be an Übermensch (super-man; badass) in the face of existential crisis. I see Active Nihilism and Absurdism as the same thing.
So, to clarify, I am an Absurdist because it is the most fun of the three aforementioned coping methods.
Lots of people say "Everything happens for a reason" to imply that every event serves a greater purpose in the future. However, the phrase literally means "Everything that happens is caused by things that happened before it", implying Determinism, which, by philosophical extension to Nihilism, is the direct opposite of their intended meaning. The result is one of the most heinously ambiguous sayings in the English language.
Assigned reading: The Myth Of Sisyphus by Albert Camus; http://en.wikipedia.org/wiki/The_Myth_of_Sisyphus
Assigned watching: Harold and Maude by Hal Ashby; http://en.wikipedia.org/wiki/Harold_and_maude