Many banana cultivars are triploid interspecific hybrids between M. acuminata (Genome A, 2n=22) and M. balbisiana (Genome B, 2n=22). They included the important group of Plantain cooking bananas classified as AAB. We compared the global chromosome structure of A and B genomes through the construction of a M. balbisiana genetic map and its comparison with the M. acuminata reference sequence assembly. We identified a large reciprocal translocation involving chromosome 1 and 3 and a large inversion on chromosome 5. We analyzed the A/B chromosomes composition of plantain cultivars revealing a few chromosome segments with AAA composition and one entire chromosome with ABB composition instead of the supposed general 'AAB' composition. We analyzed the A/B chromosomes composition of a progeny from a 'AAAB' tetraploid plantain derived breeding accession. We observed recombination between A and B genomes along most of the chromosomes. A few exceptions were observed with no recombination in the inverted segment between A and B on chromosome 5 and a reduced recombination near the translocated breakpoints on chromosome 1 and 3. We also observed a very important number of aneuploids in the progeny (62%) with 6% involving chromosome 5 and 46% involving chromosome 1 and 3, the three chromosomes that differed in their global structure between A and B genomes. Implication of these results on the origin of banana cultivars and on breeding of banana allopolyploids will be discussed.