PECVD SiC:H (SiCN:H) films were produced using tetramethylsilane (TMS) as a precursor in a mixture with inert helium or ammonia as a source of nitrogen. Mild plasma conditions were chosen in order to prevent the complete decomposition of the precursor molecules and promote the incorporation of the fragments of precursor into the film structure. The effect of deposition temperature and composition of gas mixture on the chemical bonding structure, elemental composition, deposition rate, and optical properties (transmittance, optical bandgap, and refractive index) of films have been examined. Use of the chosen deposition conditions allowed them to reach a relatively high deposition rate (up to 33 nm/min), compared with films produced in high plasma power conditions. Use of ammonia as an additional gas led to effective incorporation of N atoms in the films. The composition of the films moved from SiC:H to SiN:H with increasing of ammonia content to P(NH3)/P(TMS) = 1. The refractive index and optical bandgap of the films varied in the range of 1.55–2.08 and 3.0–5.2 eV, correspondingly, depending on the film composition and chemical bonding structure. The effect of treatment of SiCN films deposited at 400 °C by plasma of He, O2 or NH3 were studied by X-ray photoelectron spectroscopy, atomic force microscopy, and contact angle measurements. It was shown that plasma treatment significantly changes the surface characteristics. The water contact angle of the film was changed from 71 to 37° after exposure in the plasma conditions.