Neutron and X-ray reflectivity measurements are used to characterize Langmuir-Blodgett films composed of twenty bilayers of barium stearate. To facilitate contrast for neutron measurements, molecules with deuterated aliphatic tails were used for the deposition of every odd-numbered bilayer. Model fitting of both data sets shows the following : (1) the bilayer thickness is 50.4 +/- 0.1 Angstrom, consistent with an untilted aliphatic tail; (2) the area per molecule is 20.2 +/- 0.1 Angstrom(2), consistent with the area derived from pressure-area isotherms for the Langmuir layer; (3) the hydrophilic layer consists of a mixture of Ba salts and undissociated carboxylic acid groups. Its stoichiometry is given as Ba1-yH2y(COO)(2), where y=0.45 +/- 0.04; (4) neighboring bilayers are 30% intermixed, an amount too large to be explained solely by incomplete transfer coefficients during growth. Models are presented to explain the high degree of interdiffusion.