Aqueous mixtures of egg-yolk lecithin and the bile salt glycochenodeoxycholic acid sodium salt are studied using small-angle neutron scattering. Upon dilution, the shape and size of the aggregates change dramatically. This is due to very different critical micellar concentrations and spontaneous curvatures of lecithin and bile salt. At high concentrations, cylindrical micelles with a length of a few hundred angstroms are formed. As the samples are diluted, the length of the micelles first decreases and then increases by a factor of 3, their flexibility becomes noticeable, and the micelles can be described as semiflexible cylindrical micelles, also known as wormlike micelles. We have developed a mathematical model for the scattering of the wormlike micelles, which takes into account the intermicellar interaction effects. By the simultaneous fitting of the scattering data from a range of concentrations, the concentration-dependent growth law of the micelles can be parametrized. The obtained growth law of the mixed micelles is compared to the growth laws observed in simple micellar systems.