Could Hell be seen as a reward? I live in a very atheistic land. People hate religion because the main religion in my province has abused the people. Thus sometimes when I speak to friends and coworkers I present Hell as follows. 

We have been designed to love (worship) God and find our joy in Him. Heaven is where we get to love Him perfectly and enjoy Him perfectly. But a non-believer does not want to love God or enjoy Him. The non-believer wants to be God for himself. 

So if heaven is the place where God is at the center and all our attention is turned towards Him, it would go against the desire of the unbeliever's heart for God to send him to heaven. So if a person goes through life rejecting God, Hell is the place where God does not intervene (no common grace). Then does God offer the object of desire of the rebel heart?

I understand that Hell is a punishment, but does this explanation of Hell fit with the biblical teaching?
The Christian definition notion of hell itself already assumes in itself a belief in the Christian doctrines. As such, most atheists have exactly zero fear of hell, and it is considered merely an invention, typically either of fear or of control (depending on who you ask). As such, it isn't the atheists desire to exist in an afterlife without God - simply the entire notion of the afterlife is rejected.

So in answer: no, it would not be a "reward"; the mere fact of existing and have been wrong would be enough to make it miserable, even before the torment. But as I stress, atheists (and I include myself in this very completely) have no fears over this hell, or any other by any other religion. For example, I assume most Christians do not fear the hell of Jaunism, Taoism or Zoroastrianism. The atheist merely fears one less hell than most believers. To emphasise: it is not the desire of the atheist to endure an afterlife without God; the afterlife itself is unwanted.

What the atheist expects is simple: to cease to be, on the event of expiration on this world. It doesn't relate to the question, but a common follow-on question to this is "but if there is no afterlife, what reason is there to be ethical in this world?" to which the answer is simple: "there is just this world; and that by itself is plenty of reason to be ethical and face the consequences of our actions in this world that we share". Which usually works out pretty well for everyone.

Of course, if some God is truly fair to all, but ironic, they'll scupper everyone, as proposed by David Mitchell.