The guest-host liquid crystal display, first proposed in 1968, relies on controlling the orientation of dichroic dyes dissolved in a nematic liquid crystal host. Controlling the orientation of the liquid crystal and of the dissolved dye with an electric field allows control of the transmittance of the cell. Knowing the dielectric properties at optical frequencies of the dye and liquid crystal mixtures is crucial for the optimal design of guest-host liquid crystal devices. In this work, the dielectric functions of various layers in liquid crystal cells are described by models obeying the Kramers-Kronig relations: the Sellmeier equation for transparent layers and causal Gaussian oscillator model for absorbing layers. We propose a systematic way to accurately model the dielectric response of each layer by minimizing the sum of squared differences between the measured transmittance spectrum of a guest-host cell in the near-UV/vis range and the prediction of the transmittance of the modeled multilayer structure. By measuring the transmittance for incident light polarized parallel and perpendicular to the nematic director allows us to separately characterize the two principal dielectric functions of the uniaxial sample. Our results show that the causal Gaussian oscillator model can accurately characterize the dielectric functions of dyes in liquid crystals.