We describe experiments on hydrogen atoms stabilized in a 100 mu m thick H-2 film at temperatures between 0.05 and 2 K. The molecular hydrogen matrix was condensed directly from natural hydrogen gas. The H atoms are produced with a plasma discharge at temperatures below 1 K and studied with electron spin resonance. H densities of 2x10(19) cm(-3) in solid H-2 were reached. As observed earlier in thin H-2 films, we found a high stability of atomic populations and strong deviation from Boltzmann statistics of lowest two hyperfine states at the lowest temperatures. In thick films we found that the ESR resonance lines consisted of two closely spaced components with different widths indicating separate regions of high and low concentrations of H atoms in the H-2 matrix. Upon warming, the two components show very different rates of recombination with the higher density component having a faster recombination rate at T > 1 K. We discuss the atomic interactions and mobility, and also the structure of the samples of H atoms in the H-2 matrix.