Principles from human-human physical interaction may be necessary to design more intuitive and seamless robotic devices to aid human movement. Previous studies have shown that light touch can aid balance and that haptic communication can improve performance of physical tasks, but the effects of touch between two humans on walking balance has not been previously characterized. This study examines physical interaction between two persons when one person aids another in performing a beam-walking task. 12 pairs of healthy young adults held a force sensor with one hand while one person walked on a narrow balance beam (2 cm wide x 3.7 m long) and the other person walked overground by their side. We compare balance performance during partnered vs. solo beam-walking to examine the effects of haptic interaction, and we compare hand interaction mechanics during partnered beam-walking vs. overground walking to examine how the interaction aided balance. While holding the hand of a partner, participants were able to walk further on the beam without falling, reduce lateral sway, and decrease angular momentum in the frontal plane. We measured small hand force magnitudes (mean of 2.2 N laterally and 3.4 N vertically) that created opposing torque components about the beam axis and calculated the interaction torque, the overlapping opposing torque that does not contribute to motion of the beam-walker's body. We found higher interaction torque magnitudes during partnered beam-walking vs. partnered overground walking, and correlation between interaction torque magnitude and reductions in lateral sway. To gain insight into feasible controller designs to emulate human-human physical interactions for aiding walking balance, we modeled the relationship between each torque component and motion of the beam-walker's body as a mass-spring-damper system. Our model results show opposite types of mechanical elements (active vs. passive) for the two torque components. Our results demonstrate that hand interactions aid balance during partnered beam-walking by creating opposing torques that primarily serve haptic communication, and our model of the torques suggest control parameters for implementing human-human balance aid in human-robot interactions.