Model-based standardization enables adjustment for confounding of a population-averaged exposure effect on an outcome. It requires either a model for the probability of the exposure conditional on the confounders (an exposure model) or a model for the expectation of the outcome conditional on the exposure and the confounders (an outcome model). The methodology can also be applied to estimate averaged exposure effects within categories of an effect modifier and to test whether these effects differ or not. Recently, we extended that methodology for use with complex survey data, to estimate the effects of disability status on cost barriers to health care within three age categories and to test for differences. We applied the methodology to data from the 2007 Florida Behavioral Risk Factor Surveillance System Survey (BRFSS). The exposure modeling and outcome modeling approaches yielded two contrasting sets of results. In the present paper, we develop and apply to the BRFSS example two doubly robust approaches to testing and estimating effect modification with complex survey data; these approaches require that only one of these two models be correctly specified. Furthermore, assuming that at least one of the models is correctly specified, we can use the doubly robust approaches to develop and apply goodness-of-fit tests for the exposure and outcome models. We compare the exposure modeling, outcome modeling, and doubly robust approaches in terms of a simulation study and the BRFSS example. Copyright © 2012 John Wiley & Sons, Ltd.