Achieving an optimal balance between mechanical properties, dielectric properties, and thermal shock resistance presents a significant challenge in the development of advanced ceramics. This study investigates Si3N4-BN composite materials, prepared by hot-press sintering with magnesium aluminum silicate (MAS) as the sintering additive, to assess the impact of varying hexagonal boron nitride (h-BN) content on their mechanical and dielectric properties, as well as their thermal shock resistance. At an h-BN content of 20 wt%, the BN layers act as a toughening phase through a pull-out mechanism, minimally impacting the composite's density. This composition results in superior fracture toughness (7.4 MPa m1/2), high strength (598 MPa), low dielectric constants (∼6.8), and dielectric loss (∼7.4 × 10−3). Notably, after a thermal shock at 1000 °C, the composite exhibits a peak residual strength of 621 MPa, surpassing its initial strength. This enhanced performance is attributed to the formation of a dense Mg–Al–Si–B–O oxide glass layer on the surface during thermal shock, which not only repairs surface defects but also induces compressive stress. The development of the Si3N4-BN-MAS composite, with its outstanding comprehensive performance, marks a significant advancement for materials used in high-temperature wave transmission applications.