Self-assembly in aqueous mixtures of a single-chain (DTAB) and a double-chain cationic surfactant (DDAB) has been investigated with small-angle neutron scattering (SANS). Small oblate spheroidal micelles formed by DTAB grow with respect to width and length to form mixed ellipsoidal tablet-shaped micelles as an increasing fraction of DDAB is admixed into the micelles. The growth behaviour of the micelles is rationalized from the general micelle model in terms of three bending elasticity constants spontaneous curvature (H-0), bending rigidity (k(c)) and saddle-splay constant ((k(c)) over bar kc). It is found that micelles grow with respect to width, mainly as a result of decreasing k(c)H(0), and in the length direction as a result of decreasing k(c). The micelles are still rather small, i.e. about 140 angstrom in length, as an abrupt transition to large bilayer aggregates is observed. The micelle-to-bilayer transition is induced by changes in aggregate composition and is observed to occur at a mole fraction of DDAB equal to about x = 0.48 in D2O, which is a significantly higher value than previously observed for the same system in H2O (x = 0.41). An abrupt micelle-to-bilayer transition is in agreement with predictions from the general micelle model, according to which an abrupt transition from micelles to bilayers is expected to occur at xi H-0 = 1/4, where x is the thickness of the self-assembled interface, and we may conclude that H-0(D2O) > H-0(H2O) for the system DDAB/DTAB in absence of added salt. Samples with bilayers are found to be composed of bilayer disks coexisting with vesicles. Disks are found to always predominate over vesicles with mass fractions about 70-90% disks and 10-30% vesicles. Micelles, disks and vesicles are observed to coexist in a few samples close to the micelle-to-bilayer transition.