Heat dissipation is paramount in the realm of modern electronics, encompassing chips and wearable devices, whose typical candidates are the two-dimensional (2D) materials due to their superior intrinsic electrical, optical or phonon properties. However, these materials are seldom found in a freestanding state when integrated into devices, often integrated with crystalline semiconductors, metals, or flexible polymers. Thermal management strategies for such devices typically rely on a macroscopic perspective, which may lack precision. Employing the techniques of machine-learning-based interatomic potentials within DFT-level quality, together with the theory of phonon coherence and scattering from different orders, the heat transport of the 2D materials combined with substrates are investigated. Contrary to conventional expectations of hindered thermal transport, our findings reveal that the thermal conductivity of graphene remains invariant when placed on substrate. This invariance is attributed to the suppression of four-phonon scattering, a consequence of symmetry-breaking effects. The more intriguing phenomenon is the observed enhancement of thermal conductivity when germanene is placed on the substrate. This outcome defies expectations and can be attributed to the competing mechanisms: increased third-order anharmonicity and decreased fourth-order anharmonicity. Besides, an increase in coherent phonon transport due to the reduced disparities in the frequencies of various phonon modes also accounts for the enhanced thermal transport. In conclusion, our study has unveiled both the invariant and enhanced heat transport in 2D materials when combined with substrates. This investigation, driven by the microscopic phonon transport theorem, offers a fresh perspective on heat dissipation in electronic devices.