A process for the complete or partial oxidation of hydrocarbons comprises contacting a C1-C8 hydrocarbon and hydrogen peroxide in the presence of a heterogeneous catalyst under conditions suitable to convert the C1-C8 hydrocarbon to at least one corresponding C1-C8 oxygenate product, wherein the heterogeneous catalyst provides confinement and contains both Brønsted-Lowry and Lewis acid centers. Particularly useful catalysts may include, for example, metal-modified ZSM-5 and other zeolites.