We consider the problem of distributed coverage control for mobile sensor networks operating in environments cluttered with polygonal obstacles which interfere with both the navigation and sensing by the nodes. A gradient-based motion control scheme is developed to maximize the joint detection probability of random events in such mission spaces, taking into account the discontinuities that are introduced by obstacles in the sensing probability models. The optimization scheme requires only local information at each node. We also propose a modified objective function which allows a more balanced coverage when necessary. An interactive simulation environment has been developed through which we illustrate the adaptive and distributed properties of the coverage algorithm in a variety of mission spaces with obstacles.