We propose a multichannel wireless network architecture that supports nodes with differing multichannel capabilities. Both contention and contention-free medium access control (MAC) protocols are proposed for this heterogeneous multichannel network. In the contention MAC protocol, a new LRN control packet Is defined that allows a pair of nodes to re-negotiate channel selection. This relaxes the assumption that nodes can sense the carrier on all supported channels In a short period of time. We model the scheduling problem for our contention-free MAC protocol as a weighted bipartite matching problem that minimizes the sum of the completion times with polynomial time complexity. We close with an Illustration showing how the weighted bipartite matching generates a transmission schedule.