Excellent scriptural points, Jabcat. There is an earthly body and a spiritual body.
For we know that if our earthly house of this tabernacle were dissolved, we have a building of God, an house not made with hands, eternal in the heavens. 2 Cor. 5:1
See basically the entire book of 1Corinthians, particulary chapter 15. It is all about the death of the body.
Also, good to read: Hebrews chapter 4 and 5
I began to quote a bunch of scriptures, but I know we all have our own bibles. I cannot find anywhere in the scriptures that promises our earthly bodies will never die. But there is plenty of promise that we are awaiting the redemption of our body (in a new body, not natural, not made of flesh and blood, not subject to death). Jesus was obedient even unto death in order to bring many sons to glory. He did not shrink from death. He embraced/accepted it, with suffering, patience, and faith in his Father. Was he not the pattern we are to follow? I'm not saying seek death. I don't think Jesus sought death. But neither did he shrink from it in fear and unbelief. Being able to face death is of paramount importance to me in my Christian faith. And not only face my own death, but also to not be shaken (to the point of losing faith) by the death of my loved ones). If I can overcome those things through Christ in this world, overcome the fear of death and the fear of dying and the fear of losing my beloved brothers and sisters to death, that is a major part of having overcome the world (IMO). I suppose that is why I have a great distaste for the health and wealth gospel - because it is not honest IMO.