Droplet-to-bicontinuous structure transitions in a family of five-component microemulsions formed with sodium 4-(l'-heptylnonyl)benzenesulfonate, isobutyl alcohol, D20, sodium chloride, and alkanes with even carbon numbers from octane to hexadecane are probed by using small-angle neutron scattering, electrical conductivity, and NMR self-diffusion measurements. The phase behavior and structure of these microemulsions are intimately linked and depend on salinity and the chain length of the alkane. Both the range of salt concentration in which the three-phase region is observed and the range of microemulsion water volume fraction within the three-phase region decrease with decreasing alkane chain length. Further, the appearance of the three-phase region is preceded by droplet-to-bicontinuous transitions. Microemulsions not exhibiting three-phase regions become bicontinuous only when they contain equal amounts of oil and water. The coincidence of the so-called percolation thresholds as determined by using electrical conductivity and self-diffusion measurements shows that electrical conduction in a dispersion of water droplets occurs with the exchange of material between the droplets. The scattering of dilute microemulsions is interpreted by using a variety of models in which the microemulsion is treated as a dispersion of hard or attractive spheres or as a dispersion of charged ellipsoids. The effect of alkane chain length on the droplet-to-bicontinuous transitions is interpreted in terms of the droplet interaction potentials.