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Accurate measurements and physical understanding of thermal boundary resistance (R) of two-dimensional (2D) materials are imperative for effective thermal management of 2D electronics and photonics. In previous studies, heat dissipation from 2D material devices was presumed to be dominated by phonon transport across the interfaces. In this study, we find that in addition to phonon transport, thermal resistance between non-equilibrium phonons in the 2D materials could play a critical role too when the 2D material devices are internally self-heated, either optically or electrically. We accurately measure R of oxide/MoS2/oxide and oxide/graphene/oxide interfaces for three oxides (SiO2, HfO2, Al2O3) by differential time-domain thermoreflectance (TDTR). Our measurements of R across these interfaces with external heating are 2-to-4 times lower than previously reported R of the similar interfaces measured by Raman thermometry with internal self-heating. Using a simple model, we show that the observed discrepancy can be explained by an additional internal thermal resistance (Rint) between non-equilibrium phonons present during Raman measurements. We subsequently estimate that for MoS2 and graphene, Rint is about 31 and 22 m2 K/GW, respectively. The values are comparable to the thermal resistance due to finite phonon transmission across interfaces of 2D materials and thus cannot be ignored in the design of 2D material devices. Moreover, the non-equilibrium phonons also lead to a different temperature dependence than that by phonon transport. As such, our work provides important insights into physical understanding of heat dissipation in 2D material devices.