We report a hybrid atomic packing scheme comprised of a covalent-bond-mediated ``stereochemical'' structure and a densely packed icosahedron in a bulk metallic glass ${\mathrm{Pd}}_{40}{\mathrm{Ni}}_{40}{\mathrm{P}}_{20}$. The coexistence of two atomic packing models can simultaneously satisfy the criteria for both the charge saturation of the metalloid element and the densest atomic packing of the metallic elements. The hybrid packing scheme uncovers the structural origins of the excellent glass forming ability of ${\mathrm{Pd}}_{40}{\mathrm{Ni}}_{40}{\mathrm{P}}_{20}$ and has important implications in understanding the bulk metallic glass formation of metal-metalloid alloys.