Multilayer films that comprise alternating inorganic barrier and polymer layers deposited on a flexible substrate are often used to protect organic electronic devices from degradation caused by oxygen and water vapor. We tested films consisting of up to 11 inorganic silicon oxide barrier and polymer layers to characterize the water vapor permeability, solubility and diffusivity of each layer based on measurements of water sorption, transient water vapor permeation and lag times. The time-dependency of transient water vapor transmission rates (WVTR) of the structures containing a barrier-polymer-barrier sequence was also estimated using a so-called quasisteady-state (QSS) approximation. The permeability values and lag times in multilayer structures predicted by QSS approximation agreed with the values determined empirically based on time-dependent WVTR measurements. The steady-state WVTR of the multilayer barrier films was dominated by the permeability of the inorganic barrier layers, whereas the solubility coefficient and thickness of the interleaved polymer layers determined the lag times. The barrier performance and lag time of multilayer structures can be predicted using the parameters obtained from sorption measurements, thus significantly reducing the time required for experiments. The results of this study will allow us to design multilayer barrier films according to the lifetime requirements of flexible organic electronic devices.