In this paper a new dispersion model of the optical constants of amorphous solids enabled us to perform an efficient parameterization of the optical constants of diamond like carbon (DLC) thin films. The model was based on the mathematical modeling of the density of electronic states (DOS) corresponding to both the valence and conduction bands. Moreover, the existence of the sigma and pi electronic states was taken into account, i.e. two valence and two conduction bands were supposed. The imaginary and real parts of the dielectric function were then calculated by the numerical convolution of the DOS and using a corresponding Kramers-Kronig relation, respectively. According to the model the DOS as well as the optical constants were calculated from ellipsometric measurements in the range 240-830 nm and estimated even outside this range. From the parameters of the model we evaluated also the ratio of pi-to-sigma electrons and consequently the sp3-to-sp2 ratio using a known hydrogen atomic fraction. The optical constants of DLC films with addition of SiOx were determined and compared with DLC too.