Joint optimization of network coding and Aloha-based medium access control (MAC) for multi-hop wireless networks is considered. The multicast throughput is maximized subject to flow conservation and MAC achievable rate constraints to obtain the optimal transmission probabilities. The resultant optimization problem is inherently non-convex and hence difficult to solve even in a centralized manner. A successive convex approximation technique is employed to obtain a Karush-Kuhn-Tucker solution. A separable problem structure is obtained and the dual decomposition technique is adopted to develop a distributed solution. The algorithm is thus applicable to large networks, and amenable to online implementation. Numerical tests verify performance and complexity advantages of the proposed approach over existing designs.