Climbing stairs is a fundamental part of daily life, adding additional demands on the postural control system compared to level walking. Although real-world gait analysis studies likely contain stair ambulation sequences, algorithms dedicated to the analysis of such activities are still missing. Therefore, we propose a new gait analysis pipeline for foot-worn inertial sensors, which can segment, parametrize, and classify strides from continuous gait sequences that include level walking, stair ascending, and stair descending. For segmentation, an existing approach based on the hidden Markov model and a feature-based gait event detection were extended, reaching an average segmentation F1 score of 98.5% and gait event timing errors below ±10ms for all conditions. Stride types were classified with an accuracy of 98.2% using spatial features derived from a Kalman filter-based trajectory reconstruction. The evaluation was performed on a dataset of 20 healthy participants walking on three different staircases at different speeds. The entire pipeline was additionally validated end-to-end on an independent dataset of 13 Parkinson’s disease patients. The presented work aims to extend real-world gait analysis by including stair ambulation parameters in order to gain new insights into mobility impairments that can be linked to clinically relevant conditions such as a patient’s fall risk and disease state or progression.