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Atmospheric composition is an important indicator of habitability and life. The presence or absence of a large exomoon around an Earth-size exoplanet could have important consequences for planet climate stability. Thus the detection of exomoons and retrieval of information regarding atmospheric composition of Earth-size exoplanets are important goals of future exoplanet observations. Here a data analysis method is developed to achieve both goals simultaneously, based on reflection spectra of exoplanet-exomoon systems. We show that the existence of exomoons, the size of exomoons, and the concentrations of some atomic and molecular species in the atmospheres of their hosting Earth-like exoplanets can be retrieved with high levels of reliability. In addition, the method can provide well-constrained fractions of basic surface types on the targets because of the characteristic spectral features of atmospheric species and surface types in the analyzed spectral range.