In dense interstellar environments, Polycyclic Aromatic Hydrocarbons (PAHs) are likely to condense onto or integrate into water ice mantles covering dust grains. Understanding the role of ice in the photo-induced processes involving adsorbed PAHs is therefore a key issue in astrochemistry. This requires (i) the knowledge of PAH-ice interactions, i.e. PAH-ice adsorption energies and local structures at the PAH-ice interface, as well as (ii) the understanding of the fate of electrons in the PAH-ice system upon excitation. Regarding (i), in this work, we determined the lowest energy structures of PAH-ice systems for a variety of PAHs ranging from naphthalene to ovalene on three types of ice - crystalline (Ih and Ic) and amorphous (low density) - using an explicit description of the electrons and a finite-sized system. The electronic structure was determined using the Self Consistent Charge Density Functional based Tight Binding (SCC-DFTB) scheme with modified Mulliken charges in order to ensure a good description of the studied systems. Regarding (ii), the influence of the interaction with ice on the Vertical Ionisation Potentials (VIPs) of the series of PAHs was determined using the constrained SCC-DFTB scheme benchmarked against correlated wavefunction results for PAH-(H2O)n (n = 1-6, 13) clusters. The results show a deviation equal, at most, to ∼1.4 eV of the VIPs of PAHs adsorbed on ice with respect to the gas phase values. Our results are discussed in the light of experimental data and previous theoretical studies.