The management of non-native invasive species is a complex but crucial task given the potential for economic and environmental damages. For many invasions the development of socially optimal control strategies requires more than is offered by the single-species, single-control models that have dominated this area of research. We develop a general stochastic optimal control framework that accommodates multiple interacting species while accounting for uncertainty in the temporal population dynamics. This extension to the current line of bioeconomic control models allows for the design of optimal management strategies that utilize both chemical and biological controls in an environment of uncertainty and irreversibility. We demonstrate the benefits of combining chemical and biological controls in long term management strategies through a case study of the hemlock woolly adelgid infestation in the eastern United States. In this application we find that the introduction of natural predators is usually sufficient to manage the infestation, though the availability of chemical controls is important when the detection of an invasion or the subsequent response is delayed.