Community assembly is determined by a combination of historical events and contemporary processes that are difficult to disentangle, but eco‐evolutionary mechanisms may be uncovered by the joint analysis of species and genetic diversity across multiple sites. Mountain streams across Europe harbour highly diverse macroinvertebrate communities whose composition and turnover (replacement of taxa) among sites and regions remain poorly known. We studied whole‐community biodiversity within and among six mountain regions along a latitudinal transect from Morocco to Scandinavia at three levels of taxonomic hierarchy: genus, species and haplotypes. Using DNA barcoding of four insect families (>3100 individuals, 118 species) across 62 streams, we found that measures of local and regional diversity and intraregional turnover generally declined slightly towards northern latitudes. However, at all hierarchical levels we found complete (haplotype) or high (species, genus) turnover among regions (and even among sites within regions), which counters the expectations of Pleistocene postglacial northward expansion from southern refugia. Species distributions were mostly correlated with environmental conditions, suggesting a strong role of lineage‐ or species‐specific traits in determining local and latitudinal community composition, lineage diversification and phylogenetic community structure (e.g., loss of Coleoptera, but not Ephemeroptera, at northern sites). High intraspecific genetic structure within regions, even in northernmost sites, reflects species‐specific dispersal and demographic histories and indicates postglacial migration from geographically scattered refugia, rather than from only southern areas. Overall, patterns were not strongly concordant across hierarchical levels, but consistent with the overriding influence of environmental factors determining community composition at the species and genus levels.