Foundation species provide many important ecosystem functions including the provision of habitat for diverse communities, but their degradation and mortality has the potential to compromise these roles. Corals are widely recognized foundation species that create reef habitats that are hotspots for biodiversity. However, the impact of global reef degradation on overall patterns of biodiversity remains difficult to predict because of our limited knowledge of mechanistic relationships between reef structure and community composition. We examined the resilience of invertebrate abundance and biodiversity on reefs following a recent coral mass mortality event on the Caribbean coast of Panama. First, we surveyed mobile invertebrate communities at both healthy and degraded reef sites and found that dead coral habitats support invertebrate assemblages that can be more diverse and abundant than live coral habitats and that coral habitat (whether live or dead) in turn supports higher diversity and abundance than structurally simple sand areas without coral. Second, we experimentally tested mechanisms of reef habitat suitability for invertebrate colonization by manipulating coral mortality and structural complexity. We found that the abundance and species richness of mobile invertebrates were significantly affected by substrate complexity rather than whether coral was live or dead. However, we detected shifts in species identity between live and dead coral. Moreover, the sensitivity of the community to reef structural complexity indicates that the ability of degraded coral reefs to sustain invertebrate assemblages is unlikely to persist if declines in reef complexity outpace recovery of living corals to the reef. Our findings suggest that the biodiversity-sustaining function of reefs has the potential to persist following coral disturbance at the scale of entire reefs and that some metrics of community structure are therefore resilient to events of foundation species mortality.