Heterostructures enable the control of transport and recombination of charge carriers, which are either injected through electrodes, or created by light illumination. Instead of full 2D-material-heterostructures in device applications, using hybrid heterostructures consisting of 2D and 3D materials is an alternative approach to take advantage of the unique physical properties of 2D materials. In addition, 3D dielectric nanostructures exhibit useful optical properties such as broadband omnidirectional antireflection effects and strongly concentrated light near the surface. In this work, the optical properties of 2D MoS2 monolayers conformally coated on 3D Si-based nanocone (NC) arrays are investigated. Numerical calculations show that the absorption in MoS2 monolayers on SiO2 NC is significantly enhanced, compared with that for MoS2 monolayers on Si NC. The weak light confinement in low refractive index SiO2 NC leads to greater absorption in the MoS2 monolayers. The measured photoluminescence and Raman intensities of the MoS2 monolayers on SiO2 NC are much greater than those on Si NC, which supports the calculation results. This work demonstrates that 2D MoS2-3D Si nano-heterostructures are promising candidates for use in high-performance integrated optoelectronic device applications.