Some traits may be influenced by more than one genome, notably host and pathogen genomes in the case of an infectious disease. As more and more organisms are sequenced, it becomes feasible to consider simultaneous genetic analysis of pairs of organisms that jointly influence a phenotype. Including the information of both organisms' genomes in the analysis has the potential to help uncover additional important genetic variants influencing the trait and lead to a better understanding of its genetic architecture. Furthermore, interactions between the two genomes might be expected to play an important role when there has been adaptation and co-evolution, as might be expected for an infectious disease. To analyze sequence data from a pair of organisms that jointly influence a phenotype, we develop a quasi-likelihood model that accounts for genetic effects of variants from both organisms, cross-species gene-by-gene interactions, additive polygenic contributions from both organisms, and cross-species additive-by-additive polygenic effects. We employ an estimating equation approach to ensure computational feasibility for genome-wide analysis of a pair of organisms simultaneously.