We describe the development of depth-graded W/Si multilayer films prepared by magnetron sputtering for use as broad-band reflective coatings for hard x-ray optics. We have used specular and nonspecular x-ray reflectance analysis to characterize the interface imperfections in both periodic and depth-graded W/Si multilayer structures, and high-resolution transmission electron microscopy (TEM) and selected area electron diffraction (SAED) to characterize the interface structure and layer morphology as a function of depth in an optimized depth-graded multilayer. From x-ray analysis we find interface widths in the range sigma=0.275-0.35 nm for films deposited at low argon pressure (with a slight increase in interface width for multilayers having periods greater than similar to 20 nm, possibly due to the transition from amorphous to polycrystalline metal layers identified by TEM and SAED), and somewhat larger interface widths (i.e., sigma=0.35-0.4 nm) for structures grown at higher Ar pressures, higher background pressures, or with larger target-to-substrate distances. We find no variation in interface widths with magnetron power. Nonspecular x-ray reflectance analysis and TEM suggest that the dominant interface imperfection in these films is interfacial diffuseness; interfacial roughness is minimal (sigma(r)similar to 0.175 nm) in structures prepared under optimal conditions, but can increase under conditions in which the beneficial effects of energetic bombardment during growth are compromised. X-ray reflectance analysis was also used to measure the variation in the W and Si deposition rates with bilayer thickness: we find that the W and Si layer thicknesses are nonlinear with the deposition times, and we discuss possible mechanisms responsible for this nonlinearity. Finally, hard x-ray reflectance measurements made with synchrotron radiation were used to quantify the performance of optimized depth-graded W/Si structures over the photon energy range from 18 to 212 keV. We find good agreement between the synchrotron measurements and calculations made using either 0.3 nm interface widths, or with a depth-graded distribution of interface widths in the range sigma=0.275-0.35 nm (as suggested by 8 keV x-ray and TEM analyses) for a structure containing 150 bilayers, and designed for high reflectance over the range 20 keV <E <70 keV. We also find for this structure good agreement between reflectance measurements and calculations made for energies up to 170 keV, as well as for another graded W/Si structure containing 800 bilayers, designed for use above 100 keV, where the peak reflectance was measured at E=212 keV to be R=76.5+/-4% at a graze angle of theta=0.08 degrees.