This paper addresses a path planning problem where a marsupial system is assigned to collect a specified amount of information about a set of objects of interest while minimizing the likelihood of detection by an opponent's sensor. A marsupial system consists of aircraft (agents) with different capabilities. The agents are characterized by their velocities, information collection capabilities, and their effectiveness at remaining undetected. This work is motivated by surveillance missions that can be accomplished more effectively and safely by leveraging the distinct capabilities of agents in a marsupial system. The models for the agents and the environment are presented, the optimal control problem is formulated, and optimal trajectories for the marsupial system as well as characteristics of the trajectories under various mission time constraints are given.