The structure of lamellar phases of symmetric AB diblock copolymers in a thin film is investigated. We quantitatively compare the composition profiles and profiles of individual segments in self-consistent field calculations with Monte Carlo simulations in the bond fluctuation model for chain length N=32 and chi N=30. Three film thicknesses are investigated, corresponding to parallel oriented lamellae with 2 and 4 interfaces and a perpendicular oriented morphology. Taking account of capillary waves, we find good quantitative agreement between the Monte Carlo simulations and the self-consistent field calculations. However, the fluctuations of the local interfacial position are strongly suppressed by confinement and mutual interactions between lamellae.