According to an aspect of the present invention, implantable or insertable medical devices are provided which contain the following: (a) substrate having one or more depressions that contain at least one therapeutic agent and (b) a porous membrane disposed over the substrate and the one or more depressions, which regulate transport of chemical species between the therapeutic-agent-containing depressions and the exterior of the device. The substrate and the porous membrane are formed of different materials each with a different thermal expansion coefficient. Moreover, one of the substrate and the porous membrane at least partially surrounds the other. Other aspects of the present invention are directed to methods of making such medical devices, and methods of treatment using such medical devices.