I don't believe in an afterlife, although I am bringing a change of underwear. 
(Woody Allen, “Conversations with Helmholtz,” Getting Even [1971])

At first sight, this is a typical joke. The comic effect is easy to explain. It fits perfectly in Freud's and Bergson's theories.

According to Freud (Der Witz ..., Ch. VIII), the comic comes from the deception of our expectations. The first part of the sentence concerns the belief in an afterlife; I expect something abstract, scary, difficult to grasp. Then it is a story of underwear, as if the afterlife were a weekend on the seaside which I might, or might not, be invited to. I had stored energy to be able to cope with what was coming, I don't need it anymore, I laugh. 

Bersgon (Le rire) also discusses this form of the comic, where something abstract is expected and then replaced by something concrete (and underwear are most concrete). According to Bergson, the comic comes from the imposition of mechanism on life. Life is not mechanical – we need to adapt to circumstances, we need to be supple – whereas mechanism is rigid. We know we would not survive if we behaved mechanically. Thus, when we see someone acting like a machine, we laugh so as to punish him and remind ourselves we must not do this. In this case, the speaker seems to reason in a purely formal manner, as if he were not understanding what he is saying. He evokes the afterlife, and he thinks about his underwear. Again he seems to consider afterlife as a weekend on the seaside.

Freud and Bergson do not really disagree. Freud thinks he can integrate Bergson's theory into his own. Bergson would probably think the same, that Freud's theory is just an aspect of his own. Here they would both agree that the comic comes from the gap between the two parts of the sentence and the fall from the abstract to the concrete.

However, the joke here is also wit. In English, Freud's “Witz” is sometimes translated as “joke,” but that is unfortunate. The joke is comical whereas wit gives pleasure but does not necessarily produce laughter. Or, if it is comical, it uses laughter for another purpose. In fact, wit aims at expressing something that is forbidden, something that is censored. This something may be unconscious or not. It may just be improper. In any case, we derive pleasure in seeing that the censorship we impose on ourselves can be overcome. To do this, wit uses various operations. It might be double meaning, or puns, or indeed, laughter.

It wouldn't do to expand about the horrible uncertainty of what comes after death, or the prospect of nonexistence, which, as we all know, annihilates all efforts, all purposes, and turns all we do into nothingness. We would not listen to this Pascalian ramble (except in certain restricted contexts such a philosophy class, or a film by Bergman, or a religious gathering before a hearty meal). It would be unpleasant and, in fact, socially unacceptable. However, when it is turned as a joke, when the intent seems to be laughter, this sad reminder of our metaphysical uncertainty becomes altogether acceptable. We have not only the pleasure of laughing but a more subtle pleasure: the pleasure of being able to express what we could not, and of seeing that the censorship was tricked. 

Still, there is something else in Woody Allen's comical wit that is related to Freud's analysis but is not really explained by Freud. The wit here belittles the fear it expresses. Relating afterlife to a change of underwear certainly makes death less frightening.

The film Love and Death is full of such wit: “What happens after we die? Is there a hell? Is there a God? Do we live again? All right, let me ask one key question: Are there girls?” Death is represented as a tall figure clad in a white sheet armed with the traditional scythe. In young Boris' dream, it forces its prisoners to dance in a ridiculous parody of a Broadway musical. At the very end, it reappears, leading the way for Boris, who has just been executed. In passing, Boris tells his wife Sonia about his experience with death: “You remember the chicken at Trisky's? It is worse.”

The comical mechanism is the same: from the abstract, from the scary, to the most concrete, the most common. The comical effect serves wit in the sense that it makes it possible to express a fear of death that otherwise would be improper, or at least unpleasant and eventually boring. But the point is that it also belittles the fear of death. This seems to be an aspect of wit that Freud has not considered, or maybe it is an invention of Woody Allen: wit not only expresses the unconscious, or something that is censored, but also makes it less frightening or less repulsive.

To relate this kind of wit to Freud's theory, I think it is an interesting (and useful) variant of what Freud calls “tendentious wit.” The tendentious wit is directed against someone. It is a gross insult, highly aggressive (involving sex, most likely) which we would never dare to express in public. However, disguised in a double meaning, or as joke, it becomes acceptable, because after all, nothing has been said, or the intention was to make people laugh, not to insult anyone. Woody's jokes on death work the same way. We would not dare to insult death (because we are a little superstitious). But as a joke, if the joke is funny, in a comedy, this mocking of death is like a secondary effect: death is a collateral victim of laughter. And we have much pleasure in seeing death, which we fear, belittled, or disease, or the emptiness below our feet on Pascal's plank: anything we fear and fear so much that we would not dare to say anything against it.