Summary: Half of the probes on Affymetrix$^{\circledR}$ microarrays contain a single base mismatch (MM) of a known perfect match (PM) target sequence. While putatively designed to detect nonspecific binding, the MM data can also contain true signals and because of this, debates persist concerning how to best combine PM and MM data for statistical modeling purposes. Most current approaches involve either subtracting some function of MM from PM or ignoring MM altogether. Here, we describe a bivariate model that includes both PM and MM based on the mixed linear modelling framework. It directly models the correlation between PM and MM and thereby increases the power of significant gene detection. We show that the bivariate mixed model offers moderate gains in power over a comparable univariate model that ignores the MM data. The gains are more prominent when the number of replicates and the array-to-array variability is small. We apply the models to a small experiment on yeast and use the data as a basis for a Monte Carlo simulation.