Thin films of amorphous SiNH (a-SiNH) and amorphous SiNOH (a-SiNOH) synthesized by plasma-enhanced chemical vapor deposition (PECVD) are used extensively in the semiconductor industry, but little is known regarding their thermodynamic stability, and there are several long-term reliability issues for these materials. To address the stability issues, a detailed thermodynamic investigation has been conducted on a series of a-SiNH, and a-SiNOH dielectric films. High-temperature oxidative drop-solution calorimetry in molten sodium molybdate solvent at 1075K was utilized to determine the formation enthalpies from the elements and from crystalline counterparts/gaseous products. Together with entropy data derived from cryogenic heat capacity measurements, we confirmed that the incorporation of more hydrogen and oxygen leads to more negative enthalpies and Gibbs free energies of formation from elements. Coupled with FTIR structural analysis, the thermochemical data suggest that the Si-H-2 chain structure and Si-O-Si bonding configurations provide the system with extra thermodynamic stability. However, the Gibbs free energies of formation from crystalline constituents and gaseous products are either positive or nearly zero, indicating that these amorphous films are not stable against decomposition, which may cause problems in high-temperature applications.