The Hindenburg utilized aluminum flake in a nitrocellulose impregnated fabric. Materials have improved since then.
In the case of He, diffusion is inhibited by polar surfaces. For the He to diffuse through the membrane in a balloon, it has to disolve into the fabric layers prior to a barrier such as aluminum. I understand that lithium and beryllium foils have higher impermeability.
In the case of He, poly(ethylene terephthalate) is a reasonable barrier, and PET is commonly available in films (and soda bottles). It is rather polar, and serves to reduce solubility.
H is a different bird, in that it has low polarity, and different materials will aid in reduction of solubility. Butadiene-acrylonitride co-polymers have low polarity and may perform better with a low polarity gas such as H2.
The gas envelope questions are really materials science questions, and require a fair understanding of not only the mechanical properties, but even more so of the permeability, solubility and diffusivity of the copolymer you might consider.
The legality of using H2 rather than He2 may not be an issue, but even if it were, I am sure that waivers are possible.
A quick check of regs on gas balloons indicates that hydrogen may be used if the aircraft manufacturer approves the gas. So it appears there is no hard regulatory bar.
Checking with a source at NWS, who indicates their balloons are launched with H2.