We report detailed reflectance studies of the exciton-polariton structure of thin-film nanocrystalline ZnO at low temperatures and compare these data to bulk crystal behaviour. The reflectance spectra are fit using a two-band dielectric response function with a number of different models involving reflected waves in the thin-film and/or excitonic dead-layers. We present matrix forms for the solution of these models, enabling computation of the reflected intensity and other field components. The reflectance of nanocrystalline ZnO differs substantially from that of bulk material, with Fabry-Perot oscillations at energies below the transverse A exciton and above the longitudinal B exciton. Between these energies we see no evidence of anomalous waves because the strong interaction of the damped exciton with the photon leads to polaritons with substantial damping such that the Fabry-Perot oscillations are eliminated. Good agreement is found between the model and data and the importance of the polariton viewpoint in understanding the reflectance data of nanocrystalline material is clearly seen. The fits provide parameter values that can be compared to bulk crystal parameters, providing a method for quantitative analysis of the films and their potential for applications such as thin-film random lasing or polariton lasing in microcavities.