Random covalent network (RCN) theory is applied to describe the infrared spectroscopic properties of carbonaceous solids with compositions containing a mixture of aromatic, aliphatic, and diamond-like hydrocarbons. Application of this technique to carbonaceous dust is equivalent to the synthesis of solids whose structure and bonding satisfy stoicheometry while minimizing strain energy. The result involves a range of compositions compatible with carbon bonding and the hydrogen concentration incorporated in the network. In general, only a limited range of compositions is available rather than the infinite number of possible compositions expected without the inclusion of these constraints. When compositions have been defined in this way, infrared spectra may be synthesized for comparison with astronomical spectra of interstellar carbonaceous solids. Such spectra contain components corresponding to absorption by CHn groups in which n = 1-3. We find, however, that additional spectral features, not included in our simple chemical model, must be present also in dust. We give plots of such spectra in the 3100-2800 cm-1 (3.2-3.6 μm) region for comparison with infrared spectra of interstellar dust. We have also developed an RCN formalism that incorporates oxygen into the carbon network as OH groups, and we show that this inclusion introduces a strong additional absorption band in the 3300 cm-1 (3.0 μm) region.