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To disentangle genetic and environmental contributions to individual differences, classical twin models (CTMs) are predominantly used. Prior research revealed several conditions under which CTMs spawn biased heritability and environmentality estimates, including the simultaneous relevance of nonadditive genetic and shared environmental influences, the presence of assortative mating, and passive gene-environment covariance. Nuclear twin family models (NTFMs), adding information from parents of twins, can handle these conditions. Little is known, however, on the actual impact of such conditions considering the empirical properties displayed by various personality-related phenotypes. The present study therefore investigated differences between NTFMs and CTMs in terms of error-adjusted heritability and environmentality across 93 personality-relevant constructs based on data from 636 twin pairs and 320 parents. Overall, NTFMs resulted in significantly lower heritability and higher environmentality estimates, suggesting an overall overestimation of heritability in CTMs. These trends pertained to about two-thirds of the investigated constructs, but reversely directed changes were detectable under specific conditions. We discuss the extent to which the assumptions underlying CTMs might bias conclusions regarding genetic and environmental contributions to personality differences and demonstrate benefits of NTFMs. Furthermore, we provide user tutorials for implementing CTMs and NTFMs based on the open-source and user-friendly statistical program JASP. [ABSTRACT FROM AUTHOR]