Gravitational wave (GW) and electromagnetic (EM) observations of neutron-star-black-hole (NSBH) mergers can provide precise local measurements of the Hubble constant (H0), ideal for resolving the current H0 tension. We perform end-to-end analyses of realistic populations of simulated NSBHs, incorporating both GW and EM selection for the first time. We show that NSBHs could achieve unbiased 1.5%–2.4% precision H0 estimates by 2030. The achievable precision is strongly affected by the details of spin precession and tidal disruption, highlighting the need for improved modeling of NSBH mergers.