Strong coupling between hyperbolic phonon-polaritons (HP) and magnetic polaritons (MP) is theoretically studied in a hexagonal boron nitride (hBN) covered deep silver grating structure. It is found that MP in grating trenches strongly interacts with HP in an anisotropic hBN thin film, leading to a large Rabi splitting with near-perfect dual band light absorption. Numerical results indicate that MP-HP coupling can be tuned by geometric parameters of the structure. More intriguingly, the resonantly enhanced fields for two branches of the hybrid mode demonstrate unusually different field patterns. One exhibits a volume-confined Zigzag propagation pattern in the hBN film, while the other shows a field-localization near the grating corners. Furthermore, resonance frequencies of these strongly coupled modes are very robust over a wide-angle range. The angle-insensitive strong interaction of hyperbolic-magnetic polaritons with dual band intense light absorption in this hybrid system offers a new paradigm for the development of various optical detecting, sensing and thermal emitting devices.