We present results of molecular dynamics simulations of a glycerol 1-monooleate bilayer in water. The total length of analyzed trajectories is 5 ns. The calculated width of the bilayer agrees well with the experimentally measured value. The interior of the membrane is in a highly disordered fluid state. Atomic density profiles, orientational and conformational distribution functions, and order parameters indicate that disorder increases toward the center of the bilayer. Analysis of out-of-plane thermal fluctuations of the bilayer surfaces occurring at the time scale of the present calculations reveals that the distribution of modes agrees with predictions of the capillary wave model. Fluctuations of both bilayer surfaces are uncorrelated, yielding Gaussian distribution of instantaneous widths of the membrane. Fluctuations of the width produce transient thinning defects in the bilayer which occasionally span almost half of the membrane. The leading mechanism of these fluctuations is the orientational and conformational motion of head groups rather than vertical motion of the whole molecules. Water considerably penetrates the head group region of the bilayer but not its hydrocarbon core. The total net excess dipole moment of the interfacial water points toward the aqueous phase, but the water polarization profile is non-monotonic. Both water and head groups significantly contribute to the surface potential across the interface. The calculated sign of the surface potential is in agreement with that from experimental measurements, but the value is markedly overestimated. The structural and electrical properties of the water-bilayer system are discussed in relation to membrane functions, in particular transport of ions and nonelectrolytes across membranes.