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Ultrathin films and multilayers, with controlled thickness down to single atomic layers, are critical for advanced technologies ranging from nanoelectronics to spintronics to quantum devices. However, for thicknesses less than 10 nm, surfaces and dopants contribute significantly to the film properties, which can differ dramatically from that of bulk materials. For amorphous films being developed as low dielectric constant interfaces for nanoelectronics, the presence of surfaces or dopants can soften films and degrade their mechanical performance. Here we use coherent short-wavelength light to fully and nondestructively characterize the mechanical properties of individual films as thin as 5 nm within a bilayer. In general, we find that the mechanical properties depend both on the amount of doping and the presence of surfaces. In very thin (5-nm) silicon carbide bilayers with low hydrogen doping, surface effects induce a substantial softening - by almost an order of magnitude - compared with the same doping in thicker (46-nm) bilayers. These findings are important for informed design of ultrathin films for a host of nano- and quantum technologies, and for improving the switching speed and efficiency of next-generation electronics.