Understanding the stability and persistence of ecological systems is critical, particularly in an era of global change. Although relatively well understood at the level of macro-organisms, much less is known about stability in complex host-microbial systems where processes operating at multiple levels of biological organization jointly regulate the microbiome. We conducted a field experiment to examine the stability in the microbiomes of three Caribbean corals (Acropora cervicornis, Pseudodiploria strigosa, and Porites astreoides) using a pulse perturbation consisting of a large dose of broad-spectrum antibiotics to disrupt the host microbial community. We found that coral hosts continued to harbor species-specific microbiomes that persisted through time despite experimental antibiotic perturbation. Although all coral host microbiomes exhibited a high degree of resistance to disturbance, the stability of their microbial communities varied across coral host species, with P. astreoides microbiomes displaying the lowest variability and community turnover over time. Interestingly, the microbiomes of species that exhibited the greatest resistance to the experimental perturbation tended to be the least stable in co-located field surveys, which suggests that natural patterns of microbiome variability can be poor predictors of their response to perturbations. A novel stage-structured mathematical model of host-microbial dynamics helped resolve this apparent paradox by showing that post-disturbance stability depended on whether microbiome control (via antimicrobial compounds) was regulated by the coral host through host sanctioning or microbes through interference competition. Overall, our results suggest that understanding how processes that operate across multiple levels of biological organization interact to regulate microbiomes is critical to both predict and mitigate the effects of environmental variation in host-microbial systems.