Packaged photodiodes suffer from Fresnel reflection from the package window glass, especially at high angles of incidence. This has a notable impact particularly on black silicon (b-Si) photodiodes, which have extreme sensitivity. In this work, we show that by adding a simple grass-like alumina antireflection (AR) coating on the window glass, excellent omnidirectional sensitivity and high external quantum efficiency (EQE) of b-Si photodiodes can be retained. We demonstrate that EQE increases at all angles, and up to 15% absolute increases in EQE at a 70° angle of incidence compared to conventional uncoated glass. Furthermore, even at the incidence angle of 50°, the double-sided coating provides higher EQE than bare glass at normal incidence. Our results demonstrate that grass-like alumina coatings are efficient and omnidirectional AR coatings for photodiode package windows in a wide wavelength range across the visible spectrum to near-infrared radiation.