We simulated encounters between a neutron star and primordial and tidal-capture binaries. Using a three-body code, we simulated 31,000 encounters, then reran a small number of cases with a three-dimensional smoothed particle hydrodynamics (SPH) code to determine the importance of hydrodynamical effects. In the case of encounters involving a tidal-capture binary, comprising of a white dwarf and a main-sequence star, we find that most exchange encounters will produce a single merged object with the white dwarf and neutron star engulfed in a common envelope of gas donated by the main-sequence primary of the original binary. A small fraction of exchanges induce a merger of the white dwarf and main-sequence star, with this object being unbound to the neutron star, and the two objects having a large (approximately 100 km s-1) relative speed at infinity. For encounters involving a primordial binary, fewer encounters require the inclusion of hydrodynamical effects. Those involving collisions or close encounters tend to produce a binary comprised of the two merged stars (now forming one star) and the third star. The binaries produced typically have large enough separations to prevent the formation of a single merged object until subsequent stellar evolution of one of the components causes it to fill its Roche lobe. Clean exchanges produce binaries with large eccentricities; they are typically sufficiently wide to avoid circularization.