The effect of electronic correlations on the properties of materials is often profound. Layered transition metal dichalcogenides offer a family of correlated quasi-2D materials exhibiting different phases with intriguing properties, such as superconductivity, charge-density-waves, or a spin-liquid state. Their van der Waals nature permits to admix them in different layered heterostructures and induce novel exotic phases in the resulting compounds. We report a combined study using low-temperature STM, non-contact AFM and first principles DFT calculations to characterize the geometric and electronic structure of the 1H/1T TaS2 van der Waals bilayer on a 2H-TaS2 crystal. Despite the sizable interlayer separation and metallic nature of the 1H layer, positive bias voltages result in a pronounced superposition of the 1T charge density wave structure on the 1H layer. The conventional explanation relying on tunneling effects proves insufficient. We rationalize this transparency effect by the presence of a weak, although sizeable, coupling between 1H and 1T layers. Weak enough to preserve the structural properties of the constituent monolayers but strong enough to introduce hybridization between the 1T and 1H electronic bands, challenging prior understanding of the system. Our results highlight the critical role played by interlayer electronic interactions in van der Waals heterostructures to determine the final ground states of the systems. [Full article]