With the burgeoning of wearable devices and passive body/brain-computer interfaces (B/BCIs), automated stress monitoring in everyday settings has gained significant attention recently, with applications ranging from serious games to clinical monitoring. With mobile users, however, challenges arise due to other overlapping (and potentially confounding) physiological responses (e.g., due to physical activity) that may mask the effects of stress, as well as movement artifacts that can be introduced in the measured signals. For example, the classical increase in heart rate can no longer be attributed solely to stress and could be caused by the activity itself. This makes the development of mobile passive B/BCIs challenging. In this paper, we introduce PASS, a multimodal database of Physical Activity and StresS collected from 48 participants. Participants performed tasks of varying stress levels at three different activity levels and provided quantitative ratings of their perceived stress and fatigue levels. To manipulate stress, two video games (i.e., a calm exploration game and a survival game) were used. Peripheral physical activity (electrocardiography, electrodermal activity, breathing, skin temperature) as well as cerebral activity (electroencephalography) were measured throughout the experiment. A complete description of the experimental protocol is provided and preliminary analyses are performed to investigate the physiological reactions to stress in the presence of physical activity. The PASS database, including raw data and subjective ratings has been made available to the research community at http://musaelab.ca/pass-database/. It is hoped that this database will help advance mobile passive B/BCIs for use in everyday settings.