There is a growing need for systems that allow to monitor continuously the health condition of patients with chronic diseases, while allowing these patients to live their daily life as usual, at home as well as out of home. Developing such systems is now feasible based on currently available wireless transmission technologies and off-the-shelf wearable sensors, but most of the applications developed so far fall into the quantified-self movement, and can hardly be used for medical monitoring. This paper presents a general architecture for mobile bio-physical monitoring, covering all stages of data acquisition, transmission, and processing. This architecture has been designed so as to meet the expectations of the medical field (especially regarding confidentiality and dependability), while remaining open and flexible (i.e., new types of sensors or data processing algorithms can be incorporated as and when needed).