3-(1,2,4-Triazol-4-yl)adamantane-1-carboxylic acid (tradcH), a heterobifunctional organic ligand in which carboxylic acid and 1,2,4-triazole groups are united through a rigid 1,3-adamantanediyl spacer, was employed for the synthesis of a MoVI oxide organic hybrid. The ligand crystallized from water as tradcH·H2O (1), possessing a two-dimensional hydrogen-bonding network, and from ethanol as a cyclic molecular solvate with the composition (tradcH)3·2EtOH (2). Treatment of tradcH with MoO3 under hydrothermal conditions afforded a new Mo trioxide hybrid, [MoO3(tradcH)]·H2O (3), which was structurally characterized. In 3, the molybdenum atoms form a polymeric zigzag chain of {μ2-O-MoO2}n which is supported by double triazole bridges, while the carboxylic acid termini are left uncoordinated. The coordination environment of the Mo centers appears as distorted cis-{MoN2O4} octahedra. The hybrid exhibits high thermal stability (up to 270 °C) and was employed for a relatively broad scope of catalytic oxidation reactions in the liquid phase. Its catalytic behavior may be compared to a reversible mutation, featuring the best sides of homogeneous and heterogeneous catalysis. The original solid material converts into soluble active species, and the latter revert to the original material upon completion of the catalytic reaction, precipitating and allowing straightforward catalyst separation/reuse (like a heterogeneous catalyst). This catalyst was explored for a chemical reaction scope covering sulfoxidation, oxidative alcohol dehydrogenation, aldehyde oxidation, and olefin epoxidation, using hydrogen peroxide as an eco-friendly oxidant that gives water as a coproduct.