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Silicon waveguides have enabled large-scale manipulation and processing of near-infrared optical signals on chip. Yet, expanding the bandwidth of guided waves to other frequencies would further increase the functionality of silicon as a photonics platform. Frequency multiplexing by integrating additional architectures is one approach to the problem, but this is challenging to design and integrate within the existing form factor due to scaling with the free-space wavelength. Here, we demonstrate that a hexagonal boron nitride (hBN)/silicon hybrid waveguide can enable dual-band operation at both mid-infrared (6.5-7.0 um) and telecom (1.55 um) frequencies, respectively. Our device is realized via lithography-free transfer of hBN onto a silicon waveguide, maintaining near-infrared operation, while mid-infrared waveguiding of the hyperbolic phonon polaritons (HPhPs) in hBN is induced by the index contrast between the silicon waveguide and the surrounding air, thereby eliminating the need for deleterious etching of the hBN. We verify the behavior of HPhP waveguiding in both straight and curved trajectories, and validate their propagation characteristics within an analytical waveguide theoretical framework. This approach exemplifies a generalizable approach based on integrating hyperbolic media with silicon photonics for realizing frequency multiplexing in on-chip photonic systems.