Human ambulation is typically characterized during steady-state isolated tasks (e.g., walking, running, stair ambulation). However, general human locomotion comprises continuous adaptation to the varied terrains encountered during activities of daily life. To fill an important gap in knowledge that may lead to improved therapeutic and device interventions for mobility-impaired individuals, it is vital to identify how the mechanics of individuals change as they transition between different ambulatory tasks, and as they encounter terrains of differing severity. In this work, we study lower-limb joint kinematics during the transitions between level walking and stair ascent and descent over a range of stair inclination angles. Using statistical parametric mapping, we identify where and when the kinematics of transitions are unique from the adjacent steady-state tasks. Results show unique transition kinematics primarily in the swing phase, which are sensitive to stair inclination. We also train Gaussian process regression models for each joint to predict joint angles given the gait phase, stair inclination, and ambulation context (transition type, ascent/descent), demonstrating a mathematical modeling approach that successfully incorporates terrain transitions and severity. The results of this work further our understanding of transitory human biomechanics and motivate the incorporation of transition-specific control models into mobility-assistive technology.