If you see me saying that "Jesus is God", know that I mean "fully God and fully man". I'm having a hard enough time understanding Reformed theology to start dividing Jesus into pieces.
Reformed theology pushes the distinction a bit further than others. But even so, normal orthodox theology has two pieces for Christ. "Piece" isn't, of course the official term, but still, Christ is composite. He has two natures.
The history is a bit complicated. Chalcedon said "two natures in one hypostasis.” But what does that mean? There were a set of later decisions fleshing it out.
First, in the second council of Constantinople, Theodore of Mopsuestia was ruled to be heretical, even though Chalcedon itself was arguably designed to be acceptable to moderates of both Alexandrian and Antiochene approaches, which would have included him. Theodore tended to emphasize the distinctness of the human and divine. It was said that he taught only a “moral union,” though he disagreed.
But then the opposite problem developed. In the third council of Constantinople, the "monothelite" view was ruled to be heretical. The monothelites said that Christ had only one will. The council said that this was docetic. If Christ is truly human he has to have everything that a human has, including a will. So in Christ there is a human will that is separate from the will of the Logos, and also that Christ took distinct human actions. In my earlier terms, this can make Christ look like two separate actors, the Logos and a human, though I think it can be interpreted so this is not the case.
Is that what the fathers at Chalcedon intended? It's hard to know. The two-nature language came from Antiochene views such as Theodore, even though Theodore was ruled to be a heretic. So there's a pretty good argument that Constantinople 3 is a correct interpretation of Chalcedon.
So what are we left with? We now have two natures, each with their own will, taking their own actions, that form a single hypostasis. But just what does the hypostatic union mean?
With Athanasius the unity is quite clear. He saw the Logos as the only subject in Christ. It was always the Logos acting, but sometimes he acted through his human body.
But once you say that there is a separate human will and separate human actions, things get very interesting, even though they are united in one person. The problem is that what most normal people mean by "person" is an entity with its own will that acts and interacts with other people. But by that definition, there would be a separate human person. The hypostatic union begins to look pretty thin.
[later note: because of another thread I've checked more of Sproul's writings. I now think he used some confusing language, but that he is substantially orthodox on the Incarnation. Thus some of the following comments are probably wrong. However it is still the case that other traditions typically often think that Reformed theology sees more distinction between the human and divine persons than is typical. I do still think that the traditional Reformed approach would benefit by being supplemented -- but not necessarily replaced -- with N T Wright's understanding of the Incarnation.]
This is the background of the Reformed approach, which leads Sproul (and others) to say "The atonement was made by the human nature of Christ," because of course God can't die. "It’s the God-man Who dies, but death is something that is experienced only by the human nature, because the divine nature isn’t capable of experiencing death." This is pushing things fairly far in the direction of making Christ two actors.
To me this is kind of a reductio ad absurdum of this approach, since the whole point of the Incarnation for the early Church was that salvation is something that neither God nor a human being can do alone. But we're not dealing here with some kind of PCUSA liberal thing. We're dealing with the implications of the ecumenical councils, drawn by orthodox Reformed writers. Of course not all theologians draw the same conclusions. But I think Reformed theology is right, to a point. I just think it left something out.
My resolution is to start with the Reformed dedication to seeing Jesus as a real human being, in accordance of Constantinople 3, but add to it that there is a unity of action in Christ. Of course Jesus has a distinct human will and thus takes real human actions. But every action of Christ is both an action of the human Jesus and of the Logos.
Thus I would replace, or possibly explain, the statement that Christ is a single hypostasis with the statement that he is a single actor. In particular, Jesus’ death is also the death of the Logos, because the fullness of God is present in Jesus, and he is acting not just as a human, but as God. Thus salvation is a divine-human act.