The hardness of epitaxial sputter-deposited Fe(001)/Pt(001) multilayers grown on single crystal MgO(001) has been previously evaluated as a function of composition wavelength, Λ. Nanoindentation results reveal that the hardness is enhanced over that expected from a simple rule of mixtures by a factor of approximately 2.5 for bilayer spacings from 20 to 125 Å. In this paper we investigate possible causes of this hardness enhancement by determining the stress, strain, and alloying in each layer of the multilayer as a function of Λ. Accurate in-plane and out-of-plane lattice parameter measurements were obtained via x-ray diffraction using synchrotron radiation. The stress state and the extent of alloying in each layer as a function of Λ was determined by using the appropriate elastic constants for each component. The stress, strain, and amount of alloying in the Pt layer were near zero for 25≤Λ≤121 Å. The Fe layer exhibited large stresses and strains which relaxed with increasing Λ for 44≤Λ≤121 Å. For Λ=25 Å, the metastable FCC structure was adopted by the Fe film. The amount of alloying also varied from approximately 11 at.% Pt for Λ=44 Å to 5 at.% Pt for Λ=121 Å. Since the structure, film stress, amount of strain relaxation, and extent of alloying vary over this range of Λ while the hardness does not, we conclude that the hardness enhancement in these films must be controlled by other factors. Nevertheless the investigation of these basic film properties has enhanced our understanding of the structure-property relationships that give rise to strengthening in multilayer thin films.