Will all believers experience a spiritual and physical death?

The Bible teaches that mankind consists of two parts: spirit and body. Furthermore, all men and women die because of sin. Both the death of the soul and the body are included in this principle, but in both cases, there are exceptions to the principle. 

First, if a person believes in Jesus Christ (i.e., is a Christian), then that person will not experience the Second Death, which is the death of the soul:

Rev. 2:11 ‘He who has an ear, let him hear what the Spirit says to the churches. He who overcomes will not be hurt by the second death.’

Rev. 20:6 Blessed and holy is the one who has a part in the first resurrection; over these the second death has no power, but they will be priests of God and of Christ and will reign with Him for a thousand years.  

Notice in both these verses, the believer in Jesus Christ will not experience the second death, which is the Bible's term for the spirit being separated from God for eternity. The only way for a person to avoid the eternal death of the soul is to accept the sacrificial death of Jesus Christ in his or her place. Though sin leads to the death of the soul, Jesus took that penalty on our behalf so we would not experience it personally by our faith in Him.

Secondly, some believers will not experience physical death either. The death of the body was instituted by God in Genesis 3 when the Lord declared a curse on the earth. Since the physical body of Adam came from the earth, his body was cursed along with the earth. This curse requires that the body pass away so a new body may come in its place (see Genesis 3:19). 

While most human beings will experience the passing of their earthly bodies through physical death, some believers are promised to avoid that experience and pass directly from the fallen body to a new eternal body at the Resurrection (sometimes called the "rapture"). This event still satisfies the Lord’s requirement that our earthly body return to dust since we will leave it behind at the resurrection, but the soul of the individual will move directly into the new body without experience the dying process. In a sense, the old body still dies (when the soul is instantaneously removed from it), but the individual will not personally experience the dying process. Paul says it this way:

1Cor. 15:51 Behold, I tell you a mystery; we will not all sleep, but we will all be changed, 
1Cor. 15:52 in a moment, in the twinkling of an eye, at the last trumpet; for the trumpet will sound, and the dead will be raised imperishable, and we will be changed. 

So the principle that all die because of sin is still true, but in the case of Christians, all will escape spiritual death and a few will even escape experiencing physical death.