Gravitational microlensing provides a unique opportunity to probe the mass distribution of stars, black holes, and other objects in our Milky Way. However, population simulations are needed to interpret results from photometric microlensing surveys. The contribution from binary objects is often minimized or neglected in these simulations despite the high percentage of binary systems and the potential microlensing holds to probe binaries. In order to simulate the population effects of binary and multiple systems on microlensing, we add resolved binary parameters based on Duchêne and Kraus 2013 to Stellar Population Interface for Stellar Evolution and Atmospheres (SPISEA), software that simulates stellar clusters. We then inject these binaries into Population Synthesis for Compact-object Lensing Events (PopSyCLE), a package that simulates Milky Way microlensing surveys. In contrast to single-star results from PopSyCLE, we find that a significant percentage of events have a binary system as either a source or lens. We also find that the addition of binaries shifts the peak of the Einstein crossing time distribution to a 2x higher value. Binary lensing events have, on average, longer Einstein crossing times and thus significantly contaminate pools of candidate black hole lens events. As a result, microlensing searches for black holes will require larger observational samples to successfully detect astrometric microlensing signals due to black holes.