I've been a Christian for 25 years. I don't think you'll ever be completely at peace with your mortality--in the same way that riding a roller coaster is still scary even though you know it's safe.
But I've seen the difference in the way my Christian and non-Christian friends handle death, and the difference is striking.
To the religious, death is an illusion. After a short time on the earth, everybody meets up again in the afterlife. It may be sad, but not too sad.
To those who don't believe in an afterlife, death is real. When someone dies, everything about them is annihilated. A lifetime of experiences destroyed; a unique personality deleted from existence, and everyone worse-off because of it.
Sadly, the desirability of an outcome has no correlation with its likelihood.
And the funny thing is, I have never lost a minute of sleep over not having existed for those initial 14 billion years.
"The universe existed for billions of years and did just fine without you. It will probably be good for eons after you're gone. And the funny thing is, I have never lost a minute of sleep over your non-existence for those initial billions of years."
It sounds both psychopathic and psychotic.
I'm actually quoting many philosophers and authors that have said the same thing and for which I agree. For example:
http://www.goodreads.com/quotes/25647-i-do-not-fear-death-i-...
Essentially, it didn't bother you that you didn't exist 100 years ago. Think hard about why it bothers you that you won't exist 100 years from now.
In 200 years, nobody will remember you.
In 1,000 years, it will be as if you never existed. Just like 1,000 years before you were born.
"I" at any moment through out your PRESENT life, is illusion (in other words, its constantly evolving, not same or real). If you cant even pin down present life, how can you be sure of past and future.
Is it fair to be happy again? To love again? To joke about things? What will they think, looking at you continuing "life"? Even 10 years later, in the middle of a family gathering with happiness all around, a shot of guilt - will they be offended I forgot about them this time? That despite saying I never would, I've sorta moved on? How are they doing, anyways? It's joyful for them, but how do they look? Did they grow a bit more? Is their hair still long? What are they doing right now? Again, the answer is to handwave and say it's all magically perfect, and probably time dilation so we'll be dead and up there before they've even gotten through the welcome brochure. Doesn't really stop you from thinking things anyways.
Then they start piling on the "it was God's plan"/"it's for the best"/"there's a higher plan". That's the best answer to the pointless, yet burning desire to know "why?" I find this despicable, although I know many people say it out of good intention - there's really not a whole lot to say, such things fill the awkward silence. But for those that think about what they're saying for more than a second, it comes out to "be happy that a dreadful, evil, event occurred to you; the creator of the universe wishes it so and thus is an honor".
Being able to definitively answer the "why?" question was a major part of my healing. Answer it just like you would any other event; stop chasing something "meaningful" behind it.
OTOH, some people don't analyze things much. They're content to smile and say "he's so happy now, and I'll be joining him soon". This seems somewhat harmless, and might give someone hope in the end of their life, despite it being unrealistic. Sometimes you lie to people make them feel better, even though you're against lying in general.
And I certainly don't begrudge what [most] people do while bereaved - pain sucks and humans should have a basic right to deal with pain. I do find it contemptible to take advantage of their condition and sell them on a "solution".
Edit: I also find it very repulsive to treat death with positive adjectives. To take one of the worst things that plagues humanity, a completely negative experience, and then, because it's inevitable, try to gussy it up and make it not so bad, but something to look forward to.