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The potential of designing silicon-based oxide/nitride with new properties through nanostructure and chemical tuning continues to captivate researchers. In this context, while oxynitrides of Si, Ge and Si/Ge are being actively explored, N-rich alternatives to the ubiquitous Si₃N₄ end member are far less known or studied. Recently, the imide-based Si₂N₂(NH) was synthesized and found to adopt a crystalline structure analogous to that of Si₂N₂O. Here we present a DFT study of the thermochemistry of Si-N-H compounds including Si₃N₄, Si₂N₂(NH) and Si(NH)₂, focusing on their relative stability and structural polymorphism. Using density functional theory (LDA) in the static lattice approximation, and at P=0, we find that the tetragonal and monoclinic phases of Si₂N₂O are ~0.6 and ~1.4 eV above the body centered orthorhombic ground state structure, quite similar to their Si₂N₂(NH) counterparts (~0.8 and ~1.8 eV, respectively). We will elucide the analogies in the polymorphism in these oxide/imide systems in terms of their p-T phase diagrams, based on ab initio quasiharmonic phonon-derived DFT thermochemistry.