Human leukocyte antigen (HLA) genes are among the most polymorphic of our genome, as a likely consequence of balancing selection related to their central role in adaptive immunity. HLA-A and HLA-B genes were recently suggested to evolve through a model of joint divergent asymmetric selection conferring all human populations, including those with severe loss of diversity, an equivalent immune potential. However, the mechanisms by which these two genes might undergo joint evolution while displaying very distinct allelic profiles in populations are still unknown. To address this issue, we carried out extensive data analyses (among which factorial correspondence analysis and linear modeling) on 2,909 common and rare HLA-A, HLA-B, and HLA-C alleles and 200,000 simulated pathogenic peptides by taking into account sequence variation, predicted peptide-binding affinity and HLA allele frequencies in 123 populations worldwide. Our results show that HLA-A and HLA-B (but not HLA-C) molecules maintain considerable functional divergence in almost all populations, which likely plays an instrumental role in their immune defense. We also provide robust evidence of functional complementarity between HLA-A and HLA-B molecules, which display asymmetric relationships in terms of amino acid diversity at both inter- and intraprotein levels and in terms of promiscuous or fastidious peptide-binding specificities. Like two wings of a flying bird, the functional complementarity of HLA-A and HLA-B is a perfect example, in our genome, of duplicated genes sharing their capacity of assuming common vital functions while being submitted to complex and sometimes distinct environmental pressures.