As part of the study of the possibilities of using carbonate reservoirs for intra-reservoir generation of hydrogen and its subsequent storage, including in conjunction with methane, it is necessary to evaluate its interaction with host rocks. The actual experience of storing methane-hydrogen mixtures (MHM) in geological structures is limited. The growing trend in research on this topic has been noticeable in recent years. An increase in the hydrogen content in the geological environment can lead to the development of a number of negative and poorly understood processes, including diffusion losses and geochemical processes, changes in the ratios of the components of gas mixtures, and the development of corrosive effects. This article presents the first results of experimental studies of the transformation of the pore space of carbonate rocks (arenite limestones) when aged in a methane-hydrogen mixture under specified reservoir conditions typical of underground gas storage facilities. Static tests were carried out on arenite limestone samples at a constant pressure of 8 MPa at a temperature of 24 ∘C. The methods of computed tomography (CT), infrared spectroscopy (IR) and nuclear magnetic resonance (NMR) were used to control changes in the test system. The entire range of analytical work was carried out for the samples before and after the experiment. The results showed that the overall and effective porosities remained stable, possibly due to the fact that hydrogen did not significantly affect the filtration and capacitance properties. An important result was the assessment of the porosity of clays, its value increased by 2 times after exposure to MHM. Based on the results of the conducted research, the necessity of monitoring the condition of the overlapping clay strata and its integrity is substantiated. The experimental approach described above can be used in commercial oil and gas practice.