There is an energy management problem with the single membrane concept.
Imagine the object being passed through is a cube, one meter each side, in and out a volume at atmospheric pressure just ten meters under water.
To exit the membrane, against a pressure differential of one hundred thousand Newtons per square meter, and displace one cubic meter of water weighing one round ton, the cube requires an energy of one hundred kiloJoules. To do so in, say, ten seconds, requires a power of ten kilowatts.
A human being, producing around 100W of power, would need to exert himself for about twenty minutes to drive such a cube outside the membrane; being around ten times smaller in volume, he could exit himself in around two minutes.
The "membrane" must then be an active mechanism. Nano-machines creeping along the surface of the incoming body, using gecko hydrophobic pili for both traction and seal, should be good.
Inside the membrane, there needs to be a much stronger "skeleton" to oppose the pressure differential.
One could do this with a large quantity of gecko-coated flexible marbles, capable of selectively gripping one another. The marbles would need to know their own rest position and be able to communicate with one another. The distance between a geckoball's actual and rest position would be its "energy". Each geckoball would either negotiate a swap of logical positions between itself and another geckoball, if by so doing the sum of their respective energies decreased, or exert a pressure towards its rest position if, and only if, in that direction there was water or air, and nothing else. This movement would require energy, of course.
The net result would be that geckoballs would part with ease in contact with a living creature, allowing it to feel no pressure, and would flow back and reconstitute themselves behind it, requiring considerable energy, as soon as it passed through. This approach requires the membrane to be somewhat thicker than the thickest object going through, which must have no holes. A thinner membrane would require sophisticated communications and checks to stabilize pressure along the separation surface: