Doesn't immortality imply creation? Souls are created and immortal. Yet Jesus is uncreated and is thus eternal.
God the Word is an eternal spirit, eternally begotten of the eternal Father. But He took a human nature. We know by Catholic Faith that this nature was a true human nature. As such it is a created nature.
Therefore Jesus Christ has a human body and a human soul. This union of flesh and spirit is called man. Now this particular Man is the Person Jesus Christ, who possesses the spirit of God.
Jesus' human nature initially consisted of created mortal body and created immortal spirit.
His divine nature eternally consists solely of spirit.
The Person of the Word, then, possess human body, human spirit, and divine spirit.
His human soul was mortal, and thus able to be separated from his body by death.
But His eternal, divine and immortal spirit was united hypostatically and inseparably to his human body and his human soul. Thus in death, the body of Jesus, the corporeal part of his human nature, though dead and devoid of a human soul, was still united to the divine and ever living spirit of God, in the unity of Person we call the Hypostatic Union.
Thus God died, not in His divine nature, but in his human flesh. The Person of the Word died bodily (His body and soul were separated) for our sins.
The human soul of Jesus, which preached to the spirits that were in prison, was not dead, but as all human souls, was created immortal in time. It too was united inseparably to the divine spirit of God in the Person of the Word.
In the resurrection, Christ put off his bodily mortality. Christ is now and forever more immortal in His created human flesh.