We study the dynamics of the spread of an infectious disease within a population partitioned into households, and stratified into resistant and nonresistant individuals. Variability in the level of resistance between households increases the initial rate of spread of the infection, as well as the infection level at the endemic equilibrium. This phenomenon is seen even when all individuals in the population are equally likely to be resistant, and can also be predicted by including spatial clustering of resistant individuals within an improved mean-field approximation.