We report for the first time on the measurement of the correlation between the depth of shower maximum and the signal in water-Cherenkov stations for events reconstructed by both the fluorescence and the surface detectors of the Pierre Auger Observatory. Such a correlated measurement is a unique feature of a hybrid air-shower observatory and allows us to determine the purity of the cosmic-ray composition. The observed correlation in the energy range around the "ankle" lg(E/eV) = 18.5 − 19.0 differs significantly from the expectations for pure beams, indicating that the primary composition in this range is mixed, unless the hadronic interactions at these energies behave very differently than in conventional, LHC-tuned event generators.