We commonly say that Jesus died on Good Friday. This is a great simplification of what happened. It took the Church until the fifth century to figure out a defining doctrine of the nature of Christ. In the end it was decided that he combined the human and divine in one person. The human and divine are not of the same substance because the divine is spiritual and the human contains a spiritual and a physical element. So what part(s) of Jesus died on Good Friday?
The only part of Jesus that could die on Good Friday was his physical body. His spiritual being (human and divine) apparently left his dead physical body for a period and during that out of time and body existence he “preached to the spirits in prison” (1 Peter 3:19). This is a difficult passage that is supported in some sense by Jesus telling Mary Magdalene when she first encountered him after his resurrection that he had not yet returned to the Father (John 20:17). It would seem that while the spiritual parts of his person were out of his physical body they were someplace other than what we think of as heaven.
When unbelievers to ask the question, “How could your God die?” they are not only expressing an ignorance of the Trinitarian nature of God but of their own duality. Our human bodies die, of course, but our spiritual part will live until the last judgment and then after that possibly forever. Jesus temporarily sacrificed his bodily life for those who believe in his deity. His human spirit did not die any more than ours will when we die physically. This is evidenced by his resurrection body having the knowledge and memories he had before his death.
What else died on Good Friday was a simple understanding of the relationship between God and the human race. Christians have been trying to figure it out for a long time now. However, an eternal loving relationship is available to all who in faith seek it.