Mate choice is a key component of the dynamics of adaptive alleles in a population. Emphasis has been given to assortative mating where mating occurs between individuals with similar phenotypes, facilitating local adaptation and speciation. Less is known about disassortative mating (or negative assortative mating) defined by preferential pairings between individuals differing in phenotype. We investigate wing pattern polymorphism displayed by toxic butterflies (Heliconius). Their patterns are signals of toxicity learned by local predators, and enhance survival through predator avoidance and mimicry with other local toxic prey. Warning signals are often used as mating cues, driving assortative mating and speciation. However, the Amazonian species Heliconius numata maintains a stable polymorphism with multiple colour morphs coexisting within populations, a situation which mimicry alone or assortative mating cannot explain. Morphs are controlled by a single locus (supergene) formed by multiple chromosomal inversions. Using experimental mating trials we found strong disassortative mating between morphs, and showed this was mediated through female choice. The wing pattern supergene showed clear excesses of heterozygotes in natural populations, contrasting with an otherwise freely panmictic genome. This may be expected if chromosomal inversions carry recessive deleterious mutations, as is known for other supergenes, causing heterozygous advantage. Between populations, genomes were atypically undifferentiated across the continental distribution. We modelled the consequences of disassortative mating on polymorphism in spatially structured populations. Disassortative mating produced negative frequency-dependence, which favours rare morphs, including those bringing poor survival benefits (absence of local co-mimics) so long as they are recessive, which fits our empirical observations. Effective gene flow between populations was enhanced through mating benefits to recessive wing-pattern alleles, acting against population differentiation, and enhancing effective population size. Through both local and global effects on the mixing of genomes, disassortative mating at the supergene maintains adaptive polymorphism, and acts against speciation.