Widespread multifactor interactions present a significant challenge in determining risk factors of complex diseases. Several combinatorial approaches, such as the multifactor dimensionality reduction (MDR) method, have emerged as a promising tool for better detecting gene-gene (G × G) and gene-environment (G × E) interactions. We recently developed a general combinatorial approach, namely the generalized multifactor dimensionality reduction (GMDR) method, which can entertain both qualitative and quantitative phenotypes and allows for both discrete and continuous covariates to detect G × G and G × E interactions in a sample of unrelated individuals. In this article, we report the development of an algorithm that can be used to study G × G and G × E interactions for family-based designs, called pedigree-based GMDR (PGMDR). Compared to the available method, our proposed method has several major improvements, including allowing for covariate adjustments and being applicable to arbitrary phenotypes, arbitrary pedigree structures, and arbitrary patterns of missing marker genotypes. Our Monte Carlo simulations provide evidence that the PGMDR method is superior in performance to identify epistatic loci compared to the MDR-pedigree disequilibrium test (PDT). Finally, we applied our proposed approach to a genetic data set on tobacco dependence and found a significant interaction between two taste receptor genes (i.e., TAS2R16 and TAS2R38) in affecting nicotine dependence.