X-ray reflectance and film stress were measured for 12 bilayer and trilayer reflective interference coatings and compared with a single-layer Ir coating. The interference coatings comprise a base layer of W, Pt, or Ir, top layers of either C or B 4 C, and, in the case of the trilayer coatings, middle layers of either Co or Ni. The coatings were deposited by magnetron sputtering. Film stress was measured using the wafer curvature technique, while X-ray reflectance was measured at grazing incidence over the ∼0.1-10k e V energy band using synchrotron radiation. Re-measurements over a period of more than two years of both stress and X-ray reflectance were used to assess temporal stability. The X-ray reflectance of all 12 bilayer and trilayer coatings was found to be both stable over time and substantially higher than single-layer Ir over much of the energy range investigated, particularly below ∼4k e V, except near the B and C K-edges, and the Co and Ni L-edges, where we observe sharp, narrow drops in reflectance due to photo-absorption in layers containing these materials. Film stress was found to be substantially smaller than single-layer Ir in all cases as well; however, film stress was also found to change over time for all coatings (including the single-layer Ir coating). The effective area of future X-ray telescopes will be substantially higher if these high reflectance bilayer and/or trilayer coatings are used in place of single-layer coatings. Additionally, the smaller film stresses found in the bilayer and trilayer coatings relative to single-layer Ir will reduce coating-stress-driven mirror deformations. Nevertheless, as all the interference films studied here have stresses that are far from zero (albeit smaller than that of single-layer Ir), methods to mitigate such deformations must be developed in order to construct high-angular-resolution telescopes using thin mirror segments. Furthermore, unless film stress can be sufficiently stabilized over time, perhaps through thermal annealing, any such mitigation methods must also account for the temporal instability of film stress that was found in all coatings investigated here.