Jesus did not suffer eternal separation from God the Father. Since the penalty for sin is eternal separation from God, then only eternal separation from God would qualify as a sufficient punishment.
But did Jesus suffer eternal separation from God? This is questionable for two reasons. First, Jesus said that the Father never left him because he always did those things that were pleasing to the Father (John 8:29). Surely Jesus’ death on the cross was pleasing to the Father, was it not? Then there was no reason in Jesus’ life for the Father to leave him. Second, it is possible that the quotation of the first phrase of Psalm 22—“My God, my God, why hast Thou forsaken me?”—was deliberately spoken by Jesus to get the listeners to think through the Psalm and to realize that they were seeing the fulfillment of that portion of Scripture before their very eyes.
Even if Jesus were separated from the Father, it was not an eternal separation. At the very least, it was only a few minutes, from the time he cried out, “My God, My God, why hast Thou forsaken me?” until just a few minutes later, when he yielded up his spirit. There was just enough time between these two events for the bystanders to give some vinegar to drink. At the most, the separation would have been or three days, but this view cannot be supported biblically, since it is based on the idea that Jesus went to supported biblically, since it is based on the idea that Jesus went to hell. Nowhere in the Bible does it say that Jesus (that Jesus “made proclamation to the spirits now in prison [1 Peter 3:19] does not prove Jesus went to hell. Luke 16 makes it clear that communication was possible across the “great gulf” between “Abraham’s bosom” and the place of torment in the place of departed spirits. Thus, if necessary, Jesus could have “made proclamation” from Paradise across the great gulf to the spirits in the place of torment). In fact, Jesus said to the thief on the cross, “Today you will be with me in Paradise.” So where did Jesus go when he died? He went to Paradise.
Even given the conjecture that a split second of separation between Jesus and the Father was equal to the eternal separation of all human beings from God, one still ends up with a direct exchange of suffering for suffering, which amounts to a payment theory of the atonement. Of course, the two major problems with the payment theory also apply to the punishment theory. If Jesus took everyone’s punishment, then everyone should be saved (universalism). Or, if not everyone will be saved, then Jesus only suffered the punishment of certain people (limited atonement). (Michael R. Saia, Understanding the Cross: The Principle of Sacrifice in the Death of Jesus [Xulon Press, 2007], 146-47)