Many of the known planetary systems are unlike our Solar System, containing hot Jupiters or planets orbiting their host stars on eccentric or inclined orbits. One possible explanation for producing such orbits is migration driven by Kozai-Lidov oscillations, which can be induced by a companion on a sufficiently inclined orbit. Observations of protoplanetary disks can help determine whether young binary companions are inclined relative to the individual stars’ nascent planetary systems and thus could induce such migration. We used ALMA to observe continuum and CO(3-2) emission from a sample of young binary systems in Taurus-Auriga, Ophiuchus, and Lupus. The kinematics of the CO emission allows us to deduce the spatial orientation of the disks, even for disks that are near our resolution limit. Comparing the orientations of the two disks within a given binary, we find examples of both well-aligned and significantly misaligned systems. Overall, our sample shows more tendency toward alignment than would be expected from a random distribution of disk inclinations, suggesting that binary formation favors aligned systems and/or that evolution toward relative alignment has occurred within 1-2 Myr of formation.