In a previous paper, we argued that there might be and useful features originating from the interference between \ifmmode \check{C}\else \v{C}\fi{}erenkov and transition radiation. This was based on the results of the single-interface case which, however, did not allow for a quantitative comparison since the intensity of \ifmmode \check{C}\else \v{C}\fi{}erenkov radiation depends on the length of the radiator (dielectric medium), while that of the transition radiation does not. It is the purpose of this paper to furnish a quantitative description of the interference effect by considering the energy spectrum emitted by a charged particle traversing a dielectric slab of finite thickness. Even though the method of calculating the energy spectrum is rather straightforward, the resulting spectrum cannot be analyzed analytically and needs numerical computations to investigate the interference. Of particular importance is the following question: By varying the thickness of the slab, the frequency of the detected radiation, the speed of the particle, and the dielectric constant, is there any interesting interference observable in the energy spectrum (such as enhancement of \ifmmode \check{C}\else \v{C}\fi{}erenkov radiation, dips, or sharp peaks, etc.) that can be generated in the optical frequency region? We find that, below the \ifmmode \check{C}\else \v{C}\fi{}erenkov threshold, the interference between the transition radiation from the two interfaces can be either constructive or destructive, and that, above the \ifmmode \check{C}\else \v{C}\fi{}erenkov threshold, except for the region near threshold and near $\ensuremath{\beta}=1$, the interference is always destructive and the resulting energy spectrum is rather smooth (including the region near the \ifmmode \check{C}\else \v{C}\fi{}erenkov threshold). Despite the fact that our expectations were not borne out, the general expression for the energy spectrum is new as well as the numerical analysis and the discussion of various limiting cases. Furthermore, the energy spectrum due to internal reflection has structure, is linearly polarized, and can be easily measured.