In the new era of gravitational wave (GW) and multi-messenger astrophysics, the detection of a GW signal from the coalescence of a black hole – neutron star (BHNS) binary remains a highly anticipated discovery. This system is expected to be within reach of the second generation of ground-based detectors. In this context, we develop a series of versatile semi-analytical models to predict the properties of all the electromagnetic (EM) counterparts of BHNS mergers. We include the nuclear-decay-powered kilonova emission, its radio remnant, the prompt emission from the jet, and the related afterglow. The properties of these counterparts depend upon those of the outflows that result from the partial disruption of the NS during the merger and from the accretion disc around the remnant, which are necessary ingredients for transient EM emission to accompany the GW signal. We therefore define ways to relate the properties of these outflows to those of the progenitor binary, establishing a link between the binary parameters and the counterpart properties. From the resulting model, we anticipate the variety of light curves that can emerge after a BHNS coalescence from the radio up to gamma-rays. These light curves feature universal traits that are the imprint of the dynamics of the emitting outflows, but at the same time, they show a clear dependence on the BH mass and spin, but with a high degree of degeneracy. The latter can be deduced by a joint GW – EM analysis. In this paper, we perform a proof-of-concept multi-messenger parameter estimation of a BHNS merger with an associated kilonova to determine how the information from the EM counterpart can complement that from the GW signal. Our results indicate that the observation and modelling of the kilonova can help to break the degeneracies in the GW parameter space, leading to better constraints on the BH spin, for example.