It's not.

Nibbana is something to be apprehended by consciousness; death, by definition, is the cessation of consciousness. By saying death is Nibbana is like saying "no head, no headache." Well, fine, but what's the point then? It's a non-starter when it comes to life as it is actually lived, and that is what matters.

This is the Third Truth given in the First Sermon by the Buddha:

Now this, bhikkhus, for the spiritually ennobled ones, is the pain-ceasing true reality. [Nibbana] is the remainderless fading away and cessation of that same craving, the giving up and relinquishing of it, freedom from it, non-reliance on it.

--SN 56.11 (http://www.accesstoinsight.org/tipitaka/sn/sn56/sn56.011.harv.html)

It says nothing about being "free from suffering." This is a common misconception about what Buddhism says.

Nibbana is about living a life in such a way that you do not feel the need to act on your desires. The Buddha still suffered, and the Buddha still had desires (he was visited by Mara up until his death). As we see from the First Truth in the same sutta,

Now this, bhikkhus, for the spiritually ennobled ones, is the true reality which is pain: birth is painful, aging is painful, illness is painful, death is painful; sorrow, lamentation, physical pain, unhappiness and distress are painful; union with what is disliked is painful; separation from what is liked is painful; not to get what one wants is painful; in brief, the five bundles of grasping-fuel are painful.

--SN 56.11

Suffering is a fact of life, and it's true that death is the end of suffering for an individual consciousness (if you don't believe in literal rebirth), but it is most certainly NOT Nibbana.

What you're suggesting may be found in some schools of thought, but certainly not in Buddhism.