Gene-environment interactions may provide a mechanism for targeting interventions to those individuals who would gain the most benefit from them. Searching for interactions agnostically on a genome-wide scale requires large sample sizes, often achieved through collaboration among multiple studies in a consortium. Family studies can contribute to consortia, but to do so they must account for correlation within families by using specialized analytic methods. In this paper, we investigate the performance of methods that account for within-family correlation, in the context of gene-environment interactions with binary exposures and quantitative outcomes. We simulate both cross-sectional and longitudinal measurements, and analyze the simulated data taking family structure into account, via generalized estimating equations (GEE) and linear mixed-effects models. With sufficient exposure prevalence and correct model specification, all methods perform well. However, when models are misspecified, mixed modeling approaches have seriously inflated type I error rates. GEE methods with robust variance estimates are less sensitive to model misspecification; however, when exposures are infrequent, GEE methods require modifications to preserve type I error rate. We illustrate the practical use of these methods by evaluating gene-drug interactions on fasting glucose levels in data from the Framingham Heart Study, a cohort that includes related individuals.