Non-native species experience novel selection pressures in introduced environments and may interbreed with native lineages. Species introductions therefore provide opportunities to investigate repeated patterns of adaptation and introgression across replicated contact zones. Here, we investigate genetic parallelism between multiple introduced populations of the invasive marine mussel, Mytilus galloprovincialis, in the absence (South Africa and California) and presence of hybridisation with a native congener (Mytilus planulatus in Batemans Bay and Sydney Harbour, Australia). Repeatability in post-introduction differentiation from native-range populations varied between genetically distinct Atlantic and Mediterranean lineages, with Atlantic-derived introductions displaying high differentiation (maxFST>0.4) and parallelism at outlier loci. Identification of long non-coding RNA transcripts (lncRNA) additionally allowed us to clarify that parallel responses are largely limited to protein-coding loci, with lncRNAs likely evolving under evolutionary constraints. Comparisons of independent hybrid zones revealed differential introgression most strongly in Batemans Bay, with an excess of M. galloprovincialis ancestry and resistance to introgression at loci differentiating parental lineages (M. planulatus and Atlantic M. galloprovincialis). Additionally, contigs putatively introgressed with divergent alleles from a closely related species, Mytilus edulis, showed stronger introgression asymmetries compared to genome-wide trends and also diverged in parallel in both Atlantic-derived introductions. These results suggest that divergent demographic histories experienced by introduced lineages, including pre-introduction introgression, influences contemporary admixture dynamics. Our findings build on previous investigations reporting contributions of historical introgression to intrinsic reproductive architectures shared between marine lineages and illustrate that interspecific introgression history can shape differentiation between colonising populations and their hybridisation with native congeners.