  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.
