We have investigated the electronic structure of Sr14-xCaxCu24O41 (x=0; 11.5) single crystals by angle-resolved photoemission spectroscopy. A satisfactory agreement with band-structure calculations is found. The Fermi surface is observed for Sr2.5Ca11.5Cu24O41 from which we derive a charge carrier concentration between 0.15 and 0.2 holes per Cu atom at T=25 K in the ladder substructure. The chain substructures, on the other hand, act as diffraction grating for the ladder photoelectrons giving rise to incommensurate replicas of the ladder bands.