We present the results of a survey for stellar and substellar companions to 82 young stars in the nearby OB association Upper Scorpius . This survey used nonredundant aperture-mask interferometry to achieve typical contrast limits of \Delta K \sim 5-6 at the diffraction limit , revealing 12 new binary companions that lay below the detection limits of traditional high-resolution imaging ; we also summarize a complementary snapshot imaging survey that discovered 7 directly resolved companions . The overall frequency of binary companions ( \sim 35 ^ { +5 } _ { -4 } % at separations of 6-435 AU ) appears to be equivalent to field stars of similar mass , but companions could be more common among lower-mass stars than for the field . The companion mass function has statistically significant differences compared to several suggested mass functions for the field , and we suggest an alternate log-normal parameterization of the mass-function . Our survey limits encompass the entire brown dwarf mass range , but we only detected a single companion that might be a brown dwarf ; this deficit resembles the so-called “ brown dwarf desert ” that has been observed by radial-velocity planet searches . Finally , our survey ’ s deep detection limits extend into the top of the planetary mass function , reaching 8-12 M _ { Jup } for half of our sample . We have not identified any planetary companions at high confidence ( \gtrsim 99.5 % ) , but we have identified four candidate companions at lower confidence ( \gtrsim 97.5 % ) that merit additional followup to confirm or disprove their existence .