Hybridization between organisms from evolutionarily distinct lineages can have profound consequences on organism ecology, with cascading effects on fitness and evolution. Most studies of hybrid organisms have focused on organismal traits, for example various aspects of morphology and physiology. However, with the recent emergence of holobiont theory, there has been growing interest in understanding how hybridization impacts and is impacted by host-associated microbiomes. Better understanding of the interplay between host hybridization and host-associated microbiomes has the potential to provide insight into both the roles of host-associated microbiomes as dictators of host performance as well as the fundamental rules governing host-associated microbiome assembly. Unfortunately, there is a current lack of frameworks for understanding the structure of host-associated microbiomes of hybrid organisms. In this paper, we develop four conceptual models describing possible relationships between the host-associated microbiomes of hybrids and their progenitor or parent taxa. We then integrate these models into a quantitative 4H index and present a new R package for calculation, visualization, and analysis of this index. Finally, we demonstrate how the 4H index can be used to compare hybrid microbiomes across disparate plant and animal systems.