Abstract: To elucidate the etiology of a disease that may have an origin during fetal development, maternal genetic effects, offspring genetic effects and their interaction effects should each be considered. The maternal-fetal genotype (MFG) incompatibility test has been proposed to detect whether certain combinations of genes for a mother and her offspring are associated with disease risk in the offspring. The development of the MFG test focused predominantly on a bi-allelic locus. However, the study can be especially difficult at a highly-polymorphic locus, for example, HLA-DRB1, where two issues often arise. When the gene under study can influence another competing phenotype, e.g., offspring viability, the genetic association with the disease may be confounded or lead to incorrect conclusions. When some family genotype data are missing, the large numbers of alleles and their various modes of action at a multi-allelic locus make the efficient use of the information provided by incomplete families difficult. Using nuclear family genotype data composed of the parents and at least one affected offspring, I propose a v-MFG test that can assess genetic effects produced by a gene on two phenotypes simultaneously. Hence the v-MFG test adjusts the possible bias resulting from confounding of viability in disease association studies. I also describe an identical-by-state (IBS) algorithm that utilizes the IBS-types, defined from combined information of family genotypes, to accommodate incomplete families into the analysis. Through computer simulations, I show that the v-MFG test is sufficiently powerful to detect genetic association with a disease when viability is reduced. It also produces accurate genetic effect estimates for disease as well as for viability under population stratification. The v-MFG test is applied on a real data set to evaluate an MFG incompatibility effect on rheumatoid arthritis. My simulations also show that the IBS algorithm is useful to utilize incomplete families in studies at a multi-allelic locus. The IBS-types make it feasible to evaluate non-Mendelian genetic effects in one model, and the tests using IBS-types is robust to population stratification. The incomplete families can be incorporated to recover power information that would otherwise be lost and thereby to enhance statistical power.