Injecting grey hydrogen into coalbed methane formations has the potential to transform coal into a geologically temporary “H2-Battery” and a permanent “CO2-sink”. This study aims to thoroughly evaluate crucial parameters-sorption, diffusion, and matrix swelling/shrinkage-that impact grey hydrogen injection in CH4-enriched coalbed formations. In terms of sorption capacity, CO2 exhibits the highest, followed by CH4 and then H2. Sorption data affirmed that anthracite coal has a certain degree of adsorption capacity for H2, with H2 demonstrating superior diffusive gas deliverability as indicated by its diffusion coefficient, which is approximately six times higher than that of CO2. These characteristic position coal as a promising candidate for temporary H2 storage and cleaning, optimizing injectivity and depletion efficiency. Interestingly, H2 adsorption induced matrix shrinkage in coal, in contrast to other strong sorption gases such as CH4 and CO2, which resulted in matrix swellings. Matrix deformations induced by H2–CO2 mixture (grey hydrogen) injection were conducted and quantified to evaluate grey hydrogen injection in future field trials. The results reveal that the majority of directional strains indicated that when the partial pressure of CO2 in the H2–CO2 mixture is equivalent to pure CO2 pressure, the latter case induces elevated swelling strains. This finding implicitly supports the hypothesis that H2–CO2 mixture injection causes less matrix swelling than pure CO2 injection at equivalent CO2 pressure. This work provides essential parameters to illustrate an enhanced synergism among hydrogen storage, carbon sequestration, and enhance coalbed methane recovery through grey hydrogen injection in coal formations.