The Reformed Christology (doctrine of Christ) must be distinguished from the Lutheran Christology. We both have a doctrine of communication of properties (communicatio idiomatum), but they are different doctrines. The Lutherans teach that whatever can be said about the person can be said about a given nature. If, then, Jesus the person can be said to be everywhere (ubiquitous), then his humanity can be said to be everywhere. This is the ground for the Lutheran doctrine of the ubiquity (everywhereness) of Christ's humanity, so that his humanity can be said to be "in, with, and under" the elements of bread and wine in the Supper.
The Reformed have always been concerned that our Lutheran brethren tend to deify the humanity of Christ and thus tend to obliterate it. Their Christology looks to us a little too much like the Eutychian heresy. They, of course, accuse us routinely of being Nestorian. We deny that categorically. We do not separate the two natures (see below). We distinguish them. There is a considerable difference.
The Reformed doctrine of communication is that what can be said about a given nature can be said of the person. If Jesus' deity is ubiquitous, then we can say that Jesus is ubiquitous, but it doesn't follow that, therefore, Jesus' humanity is ubiquitous.
The Reformed Christology follows the Definition of Chalcedon (451) very closely. If you are not familiar with this catholic creed you should get to know it. Those attributes that are proper (belong to) to the Deity remain proper to it and those attributes proper to the humanity remain so in the incarnation.
The incarnation neither makes the humanity divine nor the divinity human. That said, we do well the heed the warning of the Chalcedon about speaking glibly about "the humanity" doing x and the deity doing y. We should speak of the person of Jesus doing x or y.
With that caveat in mind we can say that Jesus died. Because what can be said of a nature can be said of the person, Acts 20:28 says that God purchased the church with his blood. Thus Jesus' was and remains (!) true human. His humanity died. In his human nature he experienced real weakness, real suffering, hunger, pain, growth, and even ignorance.
Scripture does not deify Jesus' humanity.
Thus the Reformed orthodox distinguished different classes of knowledge. There is that which only God knows (archetypal theology), and there is that which can be known by creatures. We have what they called "pilgrim theology." Jesus, in his humanity, had a sort of pilgrim theology that they called, "the theology of union." Jesus' deity had archetypal theology, but that theology/knowledge was not communicated to the humanity or it would not be human. This is the burden of the early chapters of Hebrews.
This last bit is important because American evangelicals tend to obliterate or downplay Jesus' humanity. They do so partly out of reaction to German liberalism which tended to deny the deity of Jesus, but they also do it because it seems more pious. There is a Gnostic tendency in American religion of which American evangelicalism partakes. This is not our theology, however.
So, Jesus was in the grave until he was raised. His deity was always totally identified with his humanity and transcended it at the same time. Our Lutheran critics called this the "so called Calvinistic extra." In this case, "extra means literally "beyond." The Deity is with the humanity and beyond it. Inasmuch as the Son was sustaining the universe and cooperating with the Father in bringing all things to pass, he was doing it before the incarnation, during the incarnation, and he continues to do it in Jesus' glorification. So the deity was beyond ("extra") the humanity when the humanity was in the tomb. God the Son was where he has always been. Upon his death, Jesus' human soul (he had all the human faculties) was with his Father. At his resurrection, Jesus' rational soul was re-united with his body, as ours shall be if we die before the Lord returns.
As to the image of God, it has been traditional to identify it primarily with the intellect, but there is some reason to identify it with more than the intellect. Personally I think Scripture identifies it, to some degree anyway, with our bodies in Gen 9:1-6. We ARE body and soul. Remember, the Christian hope is the resurrection of the body (1 Cor 15; 2 Cor 4).
rsc
[Edited on 8-22-2005 by R. Scott Clark]