Many complex genetic effects, including epigenetic effects, may be expected to operate via mechanisms in the inter-uterine environment. A popular design for the investigation of such effects, including effects of parent-of-origin (imprinting), maternal genotype, and maternal-fetal genotype interactions, is to collect DNA from affected offspring and their mothers (case/mother duos) and to compare with an appropriate control sample. An alternative design uses data from cases and both parents (case/parent trios) but does not require controls. In this study, we describe a novel implementation of a multinomial modeling approach that allows the estimation of such genetic effects using either case/mother duos or case/parent trios. We investigate the performance of our approach using computer simulations and explore the sample sizes and data structures required to provide high power for detection of effects and accurate estimation of the relative risks conferred. Through the incorporation of additional assumptions (such as Hardy-Weinberg equilibrium, random mating and known allele frequencies) and/or the incorporation of additional types of control sample (such as unrelated controls, controls and their mothers, or both parents of controls), we show that the (relative risk) parameters of interest are identifiable and well estimated. Nevertheless, parameter interpretation can be complex, as we illustrate by demonstrating the mathematical equivalence between various different parameterizations. Our approach scales up easily to allow the analysis of large-scale genome-wide association data, provided both mothers and affected offspring have been genotyped at all variants of interest. Genet. Epidemiol. 35:19–45, 2011. © 2010 Wiley-Liss, Inc.