The x-ray detectors on board astrophysics space missions require optical blocking filters that are highly transparent to x-rays. The filter design typically consists of a polymeric film that is a few tens of nanometers thick coated with aluminium. Due to the large size of the filter membrane (from a few tens to a few hundred square centimeters) and the extreme aspect ratio, together with severe loading conditions during launch and different stoichiometries of the polymer that could change its mechanical properties, a characterization study of the employed material is needed. The plane strain bulge test is a well-accepted methodology for the mechanical testing of structures that are less than a micrometer thick, and especially for freestanding membranes. Unfortunately, testing such ultra-thin films is not a simple task due to residual stress and experimental uncertainty at very low pressure. In this work, the elastic properties of an extremely thin (between 45 and 415 nm) membrane made of bare polyimide and coated with aluminium were derived through adopting a combined experimental-numerical methodology based on the bulge test and numerical simulations.