This paper studies a layered erasure model for interference channels, which is a simplification of the Gaussian fading interference channel using the deterministic model approach. It is assumed that interference is one-sided, so that one of the receivers is not subject to interference. Moreover, the channel state information (CSI) is known to the receivers, but there is no CSI at transmitters (CSIT). Under these assumptions, the capacity region of the one-sided layered-erasure interference channel is completely determined for arbitrary fading statistics. Previous results of Aggarwal, Sankar, Calderbank and Poor on the capacity region or sum capacity under several interference configurations are shown to be special cases of the capacity region found in this paper.