The suppression of optical reflection from a surface is essential in many applications, ranging from displays with reduced disturbance from ambient light to high-efficiency photovoltaic cells and stable light detection and ranging (LIDAR) systems. Traditionally, antireflection (AR) surfaces are made of multilayer (ML) coatings that produce destructive interference of light beams reflected from each interface. More advanced AR surfaces are based on biomimetic nanostructures (NS) that rely on a gradation of refractive index to suppress reflection. While AR-ML coatings tend to work for restricted light wavelengths and angles of incidence, AR-NS can be broadband and omnidirectional. In addition, AR-NS can provide superhydrophobicity and self-cleaning effects. Unfortunately, AR-NS often suffer from mechanical failure, this being more critical for taller structures required for operation at longer wavelengths. Here we propose to combine ML and shorter NS to achieve an AR surface with several crucial advantages, including greater spectral and angular bandwidth and water repellency compared to only AR-ML, easier fabrication, lower scattering, and higher mechanical durability compared to only AR-NS, which requires taller structures. We present theoretical and experimental studies for combined AR-ML-NS glass surfaces operating in the visible (VIS) between 380 and 780 nm and especially at longer wavelengths in the near-infrared (NIR) at around 900 nm, where applications such as LIDAR for autonomous vehicles are of high interest. Author acknowledges financial support from the Spanish State Research Agency through the “Severo Ochoa” Programme for Centres of Excellence in R&D (CEX2019-000910-S) and Project TUNA-SURF (PID2019-106892RB-I00), Fundació Cellex, Fundació Mir-Puig, and from Generalitat de Catalunya through the CERCA Program, from AGAUR 2017 SGR1634 Peer Reviewed