Binaries harboring a millisecond pulsar (MSP) and a black hole (BH) are a key observing target for current and upcoming pulsar surveys. We model the formation and evolution of such binaries in isolation at solar metallicity using the next-generation binary population synthesis code POSYDON . We examine neutron star (NS)–BH binaries where the NS forms first (labeled NSBH), as the NS must be able to spin up to MSP rotation periods before the BH forms in these systems. We find that NSBHs are very rare and have a birth rate <1 Myr ⁻¹ for a Milky Way–like galaxy in our typical models. The NSBH formation rate is 2–3 orders of magnitude smaller than that for NS–BH binaries where the BH forms first (labeled BHNS). These rates are also sensitive to model assumptions about the supernova (SN) remnant masses, natal kicks, metallicity, and common-envelope (CE) evolution parameters. We find that 100% of NSBHs undergo a mass ratio reversal before the first SN and up to 52% of NSBHs undergo a double CE phase after the mass ratio reversal occurs. Most importantly, no NSBH binaries in our populations undergo a mass transfer phase, either stable or unstable, after the first SN. This implies that there is no possibility of pulsar spin-up via accretion, and thus MSP–BH binaries cannot form. Thus, dynamical environments and processes may provide the only formation channels for such MSP–BH binaries.