Genetic incompatibilities are an important component of reproductive isolation. Although theoretical studies have addressed their evolution, little is known about their maintenance when challenged by potentially high migration rates in secondary contact. Whereas theory predicts that recombination can erode barriers, many empirical systems have been found to retain species-specific differences despite substantial gene flow. By simulating whole genomes in individuals of hybridizing species, we find that the genetic architecture of two contrasting models of epistatic hybrid incompatibilities and the context of hybridization can substantially affect species integrity and genomic heterogeneity. In line with theory, our results show that inter-genomic incompatibilities break down rapidly by recombination but can maintain genome-wide differentiation under very limited conditions. By contrast, intra-genomic interactions that arise from genetic pathways can maintain species-specific differences even with high migration rates and gene flow, while introgression at large parts of the genome can simultaneously remain extensive, consistent with empirical observations. We discuss the importance of intra-genomic interactions in speciation and consider how this form of epistatic fitness variation is implicated and supported by other theoretical and empirical studies. We further address the relevance of replicates and knowledge of context when investigating the genomics of speciation.