As conventional silicon chips have been continuously shrinking in size and are approaching their physical limits in recent years, nanomaterials have emerged as promising candidates for next-generation integrated circuits (ICs) due to their atomic-scale dimensions. Since the thermal transport properties of materials change dramatically at nanoscale, accurate characterization of the thermophysical properties of nanomaterials is the prerequisite for application. However, thermal transport in nanoscale is significantly affected by the interface between the nanomaterials and the supported substrates: (1) the interface thermal resistance will directly affect the heat transfer performance, and (2) the solid-solid interface will further affect the inherent thermophysical properties of nanomaterials. To accurately characterize the thermophysical properties in nanoscale, we developed a dual-wavelength flash Raman (DF-Raman) method which is applicable for both suspended and supported nanomaterials without the influence of laser absorption coefficient. Based on this method, we experimentally measured the thermophysical properties of typical one-dimensional (1D) and two-dimensional (2D) nanomaterials represented by carbon nanotube (CNT) and monolayer tungsten disulfide (WS₂). By comparing the measurement results of suspended and supported cases, we found a significant reduction in the thermal conductivity of nanomaterials due to the interaction of substrate. To thoroughly understand the underlying mechanism of the interface effect, we performed molecular dynamics (MD) simulation and found that the suppression of acoustic phonons caused by phonon-substrate scattering is mainly responsible for the reduction. The degree of phonon suppression by the interface varies between materials, but is more pronounced for 2D materials mainly due to their larger contact area with the substrate. Our study provides a solid understanding of the phonon transport behavior of nanomaterials with substrate interaction and provides guidance for the thermal management of nanodevices.