The structure and properties of segmented block copolymer films of aromatic polyimide (PI) and poly(ethylene glycol) (PEG) doped with an ionic liquid are studied for potential polymer electrolyte membrane applications for fuel cells. Poly(amic acid) precursors of PI-PEG copolymers of 4,4-(hexafluoroisopropylidene) diphthalic anhydride, 4,4-(1,3-phenylenedioxy) dianiline, and bis(3-aminopropyl) terminated PEG (M-n approximate to 1500) are synthesized and then thermally imidized in membrane films, followed by swelling in ethylammonium nitrate (EAN) ionic liquid. The small-angle X-ray scattering results from the EAN-doped PI-PEG copolymer films show disordered bicontinuous phase-separated nanostructures described by Teubner-Strey theory, with the interface fractal dimension determined from the Porod equation. Thermal annealing of the EAN-doped membranes at 100-140 degrees C results in increased correlation lengths and smoother interfaces of the bicontinuous nanostructures. Such improved nanostructures lead to the increased ionic conductivity by two to five times with the maximum conductivity of 210 mS cm(-1) at 60 degrees C and 70% RH, much greater (nearly fivefold) than that of Nafion films, while maintaining the mechanical stability possibly up to 140 degrees C. Moreover, the investigation of the disordered bicontinuous phase-separated nanostructure of EAN-doped PI-PEG copolymer membranes is highly relevant to understanding the nanostructures of hydrated Nafion membranes and segmented block copolymers in general.