Recently, the hybrid wireless-optical broadband network integrating optical backbone networks, passive optical networks (PON), and wireless access networks have been proposed to provide the high-bandwidth, low-cost, and ubiquitous communication connections. In this paper, we consider the design of network coding-based multicast applications in such networks with the objective of maximizing the total network utility and minimizing the deployment cost, subject to QoS constraints. The problem is formulated as a mixed integer nonlinear programming problem and the exact solution is prohibitively complex. In order to make the problem more tractable, we develop a two-step optimization procedure that iteratively selects the optical network unit and gateways for the multicast sessions. During each iteration, two subproblems are solved, i.e., a network coding design problem for the optical network, and a user assignment and bandwidth allocation problem for the wireless network. The former is solved in a distributed way based on the Lagrangian-dual decomposition; the latter is solved based on the generalized bender decomposition. Simulation results are provided to illustrate the effectiveness of the proposed solutions.