Composite films based on poly(2,6-dimethyl-1,4-phenylene oxide) modified with a hybrid star-like polymer (1, 3, and 5 wt %) with a fullerene C60 branching center and polymer chain arms of various structures (nonpolar polystyrene and the polar poly(2-vinylpyridine)-block-poly(tert-butyl methacrylate) diblock copolymer) are investigated via small-angle neutron scattering. The data analysis for initially dry samples of the matrix polymer and composites and for samples dried after swelling in deuterated methanol shows that the latter samples fil diffusion channels, a circumstance that provides a high contrast between them and the protonated matrix. This fact allows the distribution of methanol in swollen membranes and the geometry of diffusion channels to be studied. It is found that the matrix polymer possesses highly branched channels. However, removal of the solvent from the swollen polymer results in partial disappearance of the channels and transformation of the polymer into a more homogeneous material. In the case of composites, in contrast, as the fraction of the starlike polymer is increased, a well-developed system of linear channels that survive after solvent removal is formed in the matrix.