Although emerging relay-based communication networks boast of increased transmission coverage and capacity, they currently lack schemes that optimize the simultaneous utilization of the best-quality channels, especially when such channels belong to heterogeneous frequency bands. In this article, we present a centralized oracle based on a bipartite graph model for multiband multichannel allocation, in this case, to relay nodes (RNs). We also indicate the reasons for which this technique is not viable for deployment. We then go on to develop a customized greedy heuristic, the traditional choice for distributed multiband multichannel assignment to RNs, which results in suboptimal performance. Since the greedy approach does not offer a performance-bound guarantee, we also explore a better online, distributed multiband multichannel allocation strategy by proposing a sequential algorithm based on game theory. Computer-based simulation results demonstrate that our proposed game-theoretic approach significantly outperforms the traditional distributed and centralized methods with a Nash equilibrium convergence guarantee.