[en] The dependence of the stability of single-layer graphene (SLG) sandwiched between hexagonal boron nitride bilayers (h-BN) has been described and investigated for different types of stacking in order to provide the fingerprint of the stacking order which affects the optical properties of such trilayer systems. Considering the four stacking models AAA-, AAB-, ABA-, and ABC-type stacking, the static dielectric functions (in case of parallel polarizations) for AAB-type stacking possesses maximum values, and minimum values are noticed for AAA. However, AAA-type stacking structures contribute the maximum magnetic moment while vanishing magnetic moments are observed for ABA and ABC stacking. The observed optical anisotropy and magnetic properties of these trilayer heterostructures (h-BN/SLG/h-BN) can be understood from the crystallographic stacking order and inherent crystal lattice symmetry. These optical and magnetic results suggest that the h-BN/SLG/h-BN could provide a viable route to graphene-based opto-electronic and spintronic devices. (paper)