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Binaries comprised of a neutron star (NS) and a black hole (BH) have so fareluded observations as pulsars and with gravitational waves (GWs). We model theformation and evolution of these NS+BH binaries - including pulsar evolution -using the binary population synthesis code COMPAS. We predict the presence of atotal of 50-2000 binaries containing a pulsar and a BH (PSR+BHs) in theGalactic field. We find the population observable by the next generation ofradio telescopes, represented by the SKA and MeerKAT, current (LIGO/Virgo) andfuture (LISA) GW detectors. We conclude that the SKA will observe 1-80 PSR+BHs,with 0-4 binaries containing millisecond pulsars. MeerKAT is expected toobserve 0-40 PSR+BH systems. Future radio detections of NS+BHs will constrainuncertain binary evolution processes such as BH natal kicks. We show thatsystems in which the NS formed first (NSBH) can be distinguished from thosewhere the BH formed first (BHNS) by their pulsar and binary properties. We find40% of the LIGO/Virgo observed NS+BHs from a Milky-Way like field populationwill have a chirp mass $\geq 3.0$ M$_\odot$. We estimate the spin distributionsof NS+BHs with two models for the spins of BHs. The remnants of BHNS mergerswill have a spin of $\sim$0.4, whilst NSBH merger remnants can have a spin of$\sim$0.6 or $\sim$0.9 depending on the model for BH spins. We estimate thatapproximately 25-1400 PSR+BHs will be radio alive whilst emitting GWs in theLISA frequency band, raising the possibility of joint observation by the SKAand LISA.

Modelling Neutron Star-Black Hole Binaries: Future Pulsar Surveys and Gravitational Wave Detectors