In the denser and colder (≤20 K) regions of the interstellar medium (ISM), near-infrared observations have revealed the presence of submicron-sized dust grains covered by several layers of H₂O-dominated ices and "dirtied" by the presence of other volatile species. Whether a molecule is in the gas or solid-phase depends on its binding energy (BE) on ice surfaces. Thus, BEs are crucial parameters for the astrochemical models that aim to reproduce the observed evolution of the ISM chemistry. In general, BEs can be inferred either from experimental techniques or by theoretical computations. In this work, we present a reliable computational methodology to evaluate the BEs of a large set (21) of astrochemical relevant species. We considered different periodic surface models of both crystalline and amorphous nature to mimic the interstellar water ice mantles. Both models ensure that hydrogen bond cooperativity is fully taken into account at variance with the small ice cluster models. Density functional theory adopting both B3LYP-D3 and M06-2X functionals was used to predict the species/ice structure and their BEs. As expected from the complexity of the ice surfaces, we found that each molecule can experience multiple BE values, which depend on its structure and position at the ice surface. A comparison of our computed data with literature data shows agreement in some cases and (large) differences in others. We discuss some astrophysical implications that show the importance of calculating BEs using more realistic interstellar ice surfaces to have reliable values for inclusion in the astrochemical models.