Who has Immortality, God or Man? - 1 Timothy 6:16

1 Timothy 6:16 [God] who alone is immortal and who lives in unapproachable light, whom no one has seen or can see. To him be honor and might forever. Amen

1 Corinthians 15:53 For the perishable must clothe itself with the imperishable, and the mortal with immortality.

2 Timothy 1:10 But it has now been revealed through the appearing of our Savior, Christ Jesus, who has destroyed death and has brought life and immortality to light through the gospel.

A definition of immortality according to Vine's Complete Expository Dictionary of Old and New Testament Words: "Immortality - athanasia lit., deathlessness (a, negative, thanatos, Gk. for "death"). It is rendered "immortality" in 1 Cor. 15:53,54, of the glorified body of the believer; 1 Tim. 6:16, of the nature of God."

God is Immortal:

Paul says, "Now to the King eternal, immortal, invisible, the only God, be honor and glory for ever and ever. Amen" (1 Tim. 1:17). And he speaks of God as one "who alone has immortality and dwells in unapproachable light, whom no man has ever seen or can see" (1 Tim. 6:16).

The Westminster Confession of Faith (Chapter 2.1 - Of God, and of the Holy Trinity) states:

There is but one only, living, and true God, who is infinite in being and perfection, a most pure spirit, invisible, without body, parts, or passions; immutable, immense, eternal, incomprehensible, almighty, most wise, most holy, most free, most absolute; working all things according to the counsel of his own immutable and most righteous will, for his own glory; most loving, gracious, merciful, long-suffering, abundant in goodness and truth, forgiving iniquity, transgression, and sin; the rewarder of them that diligently seek him; and withal, most just, and terrible in his judgments, hating all sin, and who will by no means clear the guilty.

By "infinite in His being" the Confession teaches God's eternality has always existed in the past and always will exist in the future. He never began to be, knows no beginning or end, no growth or age, nor will he ever cease to be (Gen. 21:33; Psa. 29:10; 45:6; 48:14; 90:2, 4; 102:25-27; Isa. 40:28; 1 Tim. 1:17).

God is not only eternal, but also unchangeable in his nature or character (immutable - Num. 23:19; 1 Sam. 15:29; Psa. 102:26; Mal. 3:6; 2 Tim. 2:13; Heb. 6:17-18; Jam. 1:17). So, this attribute emphasizes the eternal constancy of his being (or nature, character) and purpose; which in turn guarantees that he remains always one and the selfsame true God.

God is immortal. By his divine nature he can be nothing less.

Jesus is immortal:

Jesus possesses the divine attribute of immortality - the inability to die (see Did Jesus Die on the Cross?). Jesus, speaking of his body, "Destroy this temple, and I will raise it again in three days" (John 2:19-21). While Jesus was raised from the dead, it is significant that Jesus said that he would have an active role in his own resurrection: "I will raise it up." Although the Father and the Holy Spirit were also both active in the resurrection of Jesus from the dead (Rom. 8:11; 10:9); Jesus also claimed the power to lay down his life and take it up again. As John 10:17-18, teaches:

The reason my Father loves me is that I lay down my life - only to take it up again. No one takes it from me, but I lay it down of my own accord. I have authority to lay it down and authority to take it up again. This command I received from my Father.

Here Jesus speaks of a power no other human being has, that being the power to lay down his own life and the power to take it up again. Moreover, the author of Hebrews says that Jesus "has become a priest not on the basis of a regulation as to his ancestry but on the basis of the power of an indestructible life" (Heb. 7:16).

Jesus possesses the divine attribute of immortality.

Christians are Immortal:

Humanity has not only physical bodies but also immaterial spirits (Heb. 4:12; 1 Thess. 5:23 - dichotomous, bipartite). Connected to this spiritual life is the fact that we have immortality. We will not cease to exist, but will live forever. As stated in the Westminster Confession of Faith (Chapter 4.2 - Of Creation):

After God had made all other creatures, he created man, male and female, with reasonable and immortal souls, endued with knowledge, righteousness, and true holiness, after his own image; having the law of God written in their hearts, and power to fulfill it: and yet under a possibility of transgressing, being left to the liberty of their own will, which was subject unto change. Beside this law written in their hearts, they received a command, not to eat of the tree of the knowledge of good and evil; which while they kept, they were happy in their communion with God, and had dominion over the creatures.

Paul explains this truth to the Corinthians. In 1 Corinthians 15:44-49, Paul contrasts Adam with Christ. He explains, "As was the earthly man, so are those who are of the earth; and as is the man from heaven, so also are those who are of heaven" (1 Cor. 15:48). Then he expands upon this truth saying, "And just as we have borne the likeness of the earthly man, so shall we bear the likeness of the man from heaven (1 Cor. 15:49). The Reformation Study Bible makes an important note on 1 Corinthians 15:44, saying:

[N]atural body ... spiritual body. This last contrast is difficult to understand but of great importance. Paul does not have in mind a contrast between physical and nonphysical, material and immaterial. The resurrection body is a physical body, not an intangible ghost. The apostle has already used the words natural and spiritual to distinguish the individual who does not have the Holy Spirit from the one who does (2:6, 14 notes). The natural person belongs to the present age (1:20), while the spiritual person is a citizen of heaven (Phil. 3:20). Christians have received the Holy Spirit and are on that account spiritual. They have not yet received the spiritual body, the body that will be fully conformed to the life given by the Spirit.

Paul goes on to say that in a moment and a twinkling of an eye everything with be changed (1 Cor. 15:51-52; Rom. 8:18-25). We will not cease to exist in physical bodies, but we will be given imperishable bodies: "For the perishable must clothe itself with the imperishable, and the mortal with immortality" (1 Cor. 15:53).

Your question focused only upon God and Christians, so I emphasized their immortality. However, those not in Christ will also live forever after physical death, along with Satan and his demons (Matt. 25:41). However, theirs is actually eternal death - everlasting destruction (2 Thess. 1:9). Answers regarding this are also given elsewhere:

Universalism - Ephesians 1:10 and Colossians 1:20

Will all mankind eventually be saved? God's Love, Hell, and Evil

What is Reprobation?

What is Annihilationism?

Annihilationism

References

Whitlock, L. G., Sproul, R. C., Waltke, B. K., & Silva, M. The Reformation Study Bible: New King James Version. Nashville: T. Nelson, 1995.