Perhaps you may benefit from hearing my perspective as an atheist.

I think this life is the only one we've got, and I regard death as the end, full stop, after which you are basically a carcass. I am also a biology student, and I know the processes by which the remains of an organism return to nourish the earth - we get the phrase 'pushing up daisies' from this. All the soil you see with grass growing from it is the remains of dead organisms and is also full of other life - fungi, bacteria, and small animals which not only live in but contribute to the soil.

What you may be fearful of perhaps is coming face-to-face with your own mortality.

Death, being the cessation of all body function, naturally includes the brain, and when the brain goes, so do we - our personalities, our memories, all we have been. The only 'living' we do after that point is in the memories of those whose lives we have touched who continue after us. We have no consciousness after we die. If you have ever been under general anesthesia, you know what that's like - you're up one moment, then you're up the next, with absolutely no awareness of the time when you're anesthetized. Death is like permanent general anesthesia.

Most people can't imagine this. Those who can don't like the idea of a general cessation of their experience, most of the time. I certainly don't; I wish I could be alive as long as I wished, because I want to see what happens and I want to do as many things as I can. (Perhaps I'll live long enough to see mind uploading, if it's remotely feasible, but I'm generally sure it isn't, given what I know about the brain and computers.)

Don't fuss too much about black humor. Just don't do it in front of the patients. Humor is one of the world's best coping mechanisms; it is mature and healthy.

In addition, just seeing death on a frequent basis is enough to affect anyone enough to need counseling. I suggest you find some.