Polymers of intrinsic microporosity (PIMs) are a group of polymers with molecular sieve behaviour due to their rigid, contorted macromolecular backbones. They show great potential in organophilic pervaporation, solvent-resistant nanofiltration and gas and vapour separations. However, they are susceptible to physical ageing, leading to a reduction in permeability over time. An improvement in membrane permeability, control over diffusion selectivity and a reduction of the effect of physical ageing is expected by adding graphene as a nanofiller. Little is experimentally known about how the material disperses in the polymer. Here we used Raman spectroscopy, scanning transmission electron microscopy (STEM) and electron energy loss spectroscopy (EELS) to study the composite membrane's structure. Our results show that both STEM and Raman spectroscopy are able to identify the presence of graphene-based material in the composite. We show that STEM, through medium angle annular dark field (MAADF) or EELS imaging, can be exploited to obtain information on the morphology and the thickness of the flakes. Our results indicate that there is strong re-agglomeration of initially exfoliated graphene in solution when forming the composite. This is expected to produce strong changes in the mechanical properties and the physical ageing of the membrane.