Finite mixtures of regression models provide a flexible modeling framework for many phenomena including gene-gene interactions, gene-environment interactions and personalized medicine. Using moment-based estimation of the regression parameters, we develop unbiased estimators with a minimum of assumptions on the mixture components. In particular, only the average regression model for one of the components in the mixture model is needed with no requirements on the distributions, and it is not necessary to specify the mixture components further. This allows for a very flexible framework that is ideal for studying for example gene-environment interactions, where the environmental factors are otherwise unmeasured. The consistency and asymptotic distribution of the estimators is derived and the method is applied to a large-scale genome study to identify single-nucleotide-polymorphisms that were undiscovered using traditional approaches.