We present an interactive motion planning algorithm to compute plausible trajectories for high-DOF human-like characters. Given a discrete sequence of contact configurations, we use a threephase optimization approach to ensure that the resulting trajectory is collision-free, smooth, and satisfies dynamic balancing constraints. Our approach can directly compute dynamically balanced and natural-looking motions at interactive frame rates and is considerably faster than prior methods. We highlight its performance on complex human motion benchmarks corresponding to walking, climbing, crawling, and crouching, where the discrete configurations are generated from a kinematic planner or extracted from motion capture datasets.