The dynamics of water confined in various self-assembled liquid-crystalline phases of the system Dimodan U/J-R(+)-limonene-water have been investigated by dielectric relaxation spectroscopy (DRS) over a wide range of frequencies (0.2 <= nu/GHz <= 50). For all phases, two water-related Debye processes were detected, one slightly slower, the other considerably slower, than bulk water. Besides these bulk-like and slow-water relaxations, a further fraction of water does not appear in the dielectric spectra due to strong interactions with the interface (bound water). Increasing the water content of the inverse hexagonal (H-II) phase leads to an increase in both bulk-like and bound water, whereas the amount of slow water remains constant. Furthermore, the bulk-like water relaxation times accelerate until they reach the pure-water value when approaching the saturation line. This finding is supported by differential scanning calorimetry (DSC), which also confirms the presence of three types of water in liquid-crystalline confinement.