My expertise is more mechanical deformation and metallurgy. I know only the basics regarding radiation.
But here goes
The mechanism they are employing is ionization (in this case, forming a cation by losing an electron through a high energy particle collision). The susceptibility to such ionization is measured (and on most Periodic Tables) as the first Ionization Potential. The ionization potential, I, of an atom is basically the energy that the gaseous atom must absorb in order for its most loosely held electron to become separated. As a general rule, ionization energies decrease as the size of the atoms increase (ie the loosest electron is less tightly bound in a big atom).
I assume they are using H2 to target higher energies typical of gamma rays. (the ionization potential of H is 13.598 eV). Sounds like they are creating their "composite" by bubbling H2 while forming the polyethylene sheet. Think of a miniaturized "bubble wrap" with H2 instead of air.
This type of shielding would gradually loose effectiveness as more and more H2 is ionized.