Thanks for the answers, everyone.
Another related and probably overly analytical question:
If body and soul are separated at death, what happened at Christ's death? Did both His body and His soul stay united to the divine nature although they were separate?
Yes. After the Word became flesh, His human and divine natures became inseparable and indivisible, but also unmingling, without confusion, and without alteration. Likewise, in one of the troparia of the Paschal hours, we say, "In the grave bodily, but in hades with Thy soul as God: in Paradise with the thief, and on the throne with the Father and the Spirit wast Thou Who fillest all things, O Christ the Inexpressible."
We don't endeavor to explain the paradoxes, they are inexplicable. Rather, we embrace them.