To deliver user traffic in a wireless mesh network, mesh stations equipped with multiple wireless interfaces communicate with one another utilizing multiple orthogonal channels. Channel assignment in such an environment is to assign one channel to each interface to minimize co-channel interference among wireless links while preserving link connectivity. The interference and connectivity objectives are generally conflicting. This paper proposes a game-theoretic approach that jointly considers the two objectives with a unified payoff function. We prove that the proposed approach is an exact potential game, which guarantees stability in a finite time. We also prove the link-preserving property of the approach. Simulation results show that the proposed approach generally outperforms counterparts in terms of network interference when a moderate number of channels are available.