Genes can be associated with disease through an individual's inherited genotype, the maternal genotype or the interaction between these two. When the gene is highly polymorphic, it is more difficult to identify the gene's functional role than for less polymorphic loci, because different alleles at the locus may be associated with the disease through separate and joint effects from maternal and offspring genotypes. Family-based studies are used to test genetic associations because of their robustness to population stratification. However, parental genotype data are often missing, and omitting incompletely genotyped families is inefficient. Methods have been proposed to accommodate incomplete families in family-based association studies. They are not easily generalized to allow simultaneous examination of offspring allelic, maternal allelic and maternal-fetal genotype (MFG) incompatibility effects. Since many MFG incompatibility effects occur through matching between maternal and offspring's genotypes, we present an identity-by-state (IBS) framework to incorporate incomplete families in the MFG test when modeling genetic effects produced by a polymorphic gene. Using simulations, we examine the MFG test's performance with incomplete parental genotype data and an IBS framework. The MFG test using the IBS framework is immune to population stratification and efficiently uses information from incomplete families.