Have you ever heard of goldbeater's skin? This was the preferred material before synthetic materials became available.
What is it? Wikipedia says:
Goldbeater's skin—the outer membrane of a calf's intestine—is a
parchment traditionally used in the process of making gold leaf by
beating, reducing gold into mere 1 μm-thick leaves. […] To manufacture goldbeater's skin, the gut of oxen (or other cattle) is soaked in a dilute solution of potassium hydroxide, washed, stretched, beaten flat and thin, and treated chemically to prevent putrefaction.
From the 1880's on it became the preferred material for gas bags, displacing rubberized cloth or silk which would become brittle quickly. The first man-carrying hydrogen ballon used already silk which had been rubberized by varnishing it with rubber that had been dissolved in turpentine. Again Wikipedia:
Large quantities of goldbeater's skin were used to make the gas bags
of early balloons created by the Royal Engineers at Chatham, Kent
starting in 1881–82 culminating in 1883 with "The Heron", of 10,000 cu
ft capacity. The method of preparing and making gas-tight joins in the
skins was known only to a family from Alsatia called Weinling who were
employed by the RE for many years. The British had a monopoly on the
technique until around 1912 when the Germans adopted the material for
the internal gas bags of the "Zeppelin" rigid airships, exhausting the
available supply: about 200,000 sheets were used for a typical World
War I Zeppelin, while the USS Shenandoah needed 750,000 sheets. The
sheets were joined together and folded into impermeable layers.
There is a more detailed description in the Wikipedia article on the ZR-1 which reveals that the goldbeater's skin was reinforced with cotton cloth:
The gas cells were made of goldbeater's skins, one of the most
gas-impervious materials known at the time. Named for their use in
beating and separating gold leaf, goldbeater's skins were made from
the outer membrane of the large intestines of cattle. The membranes
were washed and scraped to remove fat and dirt, and then placed in a
solution of water and glycerine in preparation for application to the
rubberized cotton fabric providing the strength of the gas cells.
The membranes were wrung out by hand to remove the water-glycerine
storage solution and then rubber-cemented to the cotton fabric and
finally given a light coat of varnish.
Today the preferred material is polyethylene therephtalate, a polyester, which is also used for blister packages or soda bottles. By itself, it would have far too high a rate of permeation, therefore it is sealed with a metallic layer of a thickness of only a few atoms. Such metallized films are also used for thermal blankets, in spacesuits, on satellites and for toy helium balloons. To increase its tensile strength, the film is stretched in two perpendicular directions such that the molecule chains become elongated and the film becomes thinner. The result is called biaxially oriented PET (BoPET) and metallized by vapor deposition of a thin layer of aluminium.