  Observations by the current generation of gravitational-wave detectors have
been pivotal in expanding our understanding of the universe. Although tens of
exciting compact binary mergers have been observed, neutron star-black hole
(NSBH) mergers remained elusive until they were first confidently detected in
2020. The number of NSBH detections is expected to increase with sensitivity
improvements of the current detectors and the proposed construction of new
observatories over the next decade. In this work, we explore the NSBH detection
and measurement capabilities of these upgraded detectors and new observatories
using the following metrics: network detection efficiency and detection rate as
a function of redshift, distributions of the signal-to-noise ratios, the
measurement accuracy of intrinsic and extrinsic parameters, the accuracy of sky
position measurement, and the number of early-warning alerts that can be sent
to facilitate the electromagnetic follow-up. Additionally, we evaluate the
prospects of performing multi-messenger observations of NSBH systems by
reporting the number of expected kilonova detections with the Vera C. Rubin
Observatory and the Nancy Grace Roman Space Telescope. We find that as many as
$\mathcal{O}(10)$ kilonovae can be detected by these two telescopes every year,
depending on the population of the NSBH systems and the equation of state of
neutron stars.
