Self-assembled cylindrical aggregates of amphiphilic carbocyanine dye molecules are interesting candidates for synthetic light-harvesting systems and electronic energy transport wires. To be able to optimize the properties of such systems, detailed information on the molecular structure as well as the static and dynamic optical properties is required. We report cryo-transmission electron microscopy (cryo-TEM) experiments on 3,3'-bis(3-sulfopropyl)-5,5',6,6'-tetrachloro-1,1'-dioctylbenzimidacarbo cyanine (C8S3) aggregates that reveal a double-layer tubular structure. By combining these results with information from both isotropic and polarized spectral responses, a detailed molecular picture of these aggregates is obtained. The basis of our theoretical analysis of the spectroscopic data is the formation of the inner and outer cylinders by rolling cyanine sheets with a brick-layer structure onto cylindrical surfaces with diameters of 11 and 16 run. This model very well reproduces the spectral properties of the excitonic transitions of the C8S3 aggregates. The combination of experimental and theoretical techniques for the first time provides detailed insight into the molecular arrangement inside these aggregates.