A multivariate binomial/multinomial model is proposed for estimating poverty and housing-unit characteristics of small areas. It is demonstrated that the model is in concordance with the design in that the model can reproduce within small area design-based estimates of variance. The methodology for producing estimates is presented, along with several evaluations using data from the American Community Survey. It is concluded that this approach can be a viable way to make small area estimates without needing to assume that the design-based estimates of variance are fixed (as in most area-level models).