Two-dimensional diffusion in heterogenic composite membranes, i.e., materials comprising polymer with dispersed inorganic fillers, composed of ethylcellulose and magnetic powder is studied. In the experimental part, the morphology of membranes is described by the following characteristics: the amount of polymer matrix, the fractal dimension of polymer matrix, the average size of polymer matrix domains, the average number of obstacles in the proximity of each polymer matrix pixel. The simulation work concentrates on the motion of a particle in the membrane environment. The focus is set on the relationship between membranes morphology characterized by polymer matrix density, its fractal dimension, the average size of domains, and the average number of near obstacles and the characteristics of diffusive transport in them. The comparison of diffusion driven by Gaussian random walk and Lévy flights shows that the effective diffusion exponent at long time limits is subdiffusive and it does not depend on the details of the underlying random process causing diffusion. The analysis of the parameters describing the membrane structure shows that the most important factor for the diffusion character is the average size of a domain penetrated by diffusing particles. The presented results may be used in the design and preparation of membrane structures with specific diffusion properties.