In this paper we develop a novel discrete choice demand model for horizontally and vertically differentiated products, with consumer preferences for products modelled over both an unordered, horizontal “brand” dimension, and an ordered, vertical “quality” dimension. This allows the model to capture important features of consumer substitution patterns when both kinds of differentiation are present. The unordered-ordered discrete nature of the two dimensions of the individual decision problem typically results in set identification of model parameters. We use the structure of the choice problem to characterize the identified set. Our characterizations can potentially be used to lead to a significant dimension-reduction in searching over the parameter space in constructing set estimates or confidence sets, and are compatible with recently developed techniques for inference via maximum likelihood when point identification fails such as those of Liu and Shao (2003) and Chen, Tamer, and Torgovitsky (2012). Joint with Adam Rosen.