Many complex genetic influences, 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 maternal genotype and maternal-foetal interactions, is to collect DNA from affected offspring and their mothers. This design can also be used for the investigation of parent-oforigin (imprinting) effects, although greater efficiency may be achievable via the additional collection of DNA from fathers, where possible. Here we propose a novel multinomial modelling approach that allows the estimation of complex genetic effects of this type using data from either case/mother duos or case/parent trios. Through the incorporation of additional assumptions (such as HardyWeinberg equilibrium, random mating and known allele frequencies) and/or the incorporation of additional control samples (such as unrelated controls, controls and their mothers, or both parents of controls), we show that the parameters of interest are identifiable and well-estimated by our method. We investigate the required sample sizes and data structures necessary to provide accurate estimation of such effects and high power for their detection. Our method is illustrated by application to data on several candidate genes involved in congenital cardiovascular malformation.