Detections of gravitational waves (GWs) may soon uncover the signal from the coalescence of a black hole - neutron star (BHNS) binary, that is expected to be accompanied by an electromagnetic (EM) signal. In this paper, we present a composite semi-analytical model to predict the properties of the expected EM counterpart from BHNS mergers, focusing on the kilonova emission and on the gamma-ray burst afterglow. Four main parameters rule the properties of the EM emission: the NS mass $M_mathrm{NS}$, its tidal deformability $Lambda_mathrm{NS}$, the BH mass and spin. Only for certain combinations of these parameters an EM counterpart is produced. Here we explore the parameter space, and construct light curves, analysing the dependence of the EM emission on the NS mass and tidal deformability. Exploring the NS parameter space limiting to $M_mathrm{NS}-Lambda_mathrm{NS}$ pairs described by a physically motivated equations of state (EoS), we find that the brightest EM counterparts are produced in binaries with low mass NSs (fixing the BH properties and the EoS). Using constraints on the NS EoS from GW170817, our modeling shows that the emission falls in a narrow range of absolute magnitudes. Within the range of explored parameters, light curves and peak times are not dissimilar to those from NSNS mergers, except in the B band. The lack of an hyper/supra-massive NS in BHNS coalescences causes a dimming of the blue kilonova emission in absence of the neutrino interaction with the ejecta.
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