This paper focuses on the problem of deploying a set of autonomous robots to efficiently monitor multiple types of events in an environment. There is a density function over the environment for each event type representing the weighted likelihood of the event at each location. The robots are heterogeneous in that each robot is equipped with a set of sensors and it is capable of sensing a subset of event types. The objective is to deploy the robots in the environment to minimize a linear combination of the total sensing quality of the events. We propose a new formulation for the problem which is a natural extension of the homogeneous problem. We propose distributed algorithms that drive the robots to locally optimal positions in both continuous environments that are obstacle-free, and in discrete environments that may contain obstacles. In both cases we prove convergence to locally optimal positions. We provide extension to the case where the density functions are unknown prior to the deployment in continuous environments. Finally, we present benchmarking results and physical experiments to characterize the solution quality.