Multihop wireless networks in which each node is equipped with multiple wireless NICs can utilize multiple wireless channels to improve performance. But how to assign wireless channels to interfaces to avoid collisions extremely while the network keeps a good topology is a problem not well solved for such a multi-NIC multihop wireless network. We reexamine the general requirements of this problem and propose an algorithm to solve it effectively and efficiently. We regard it as a particular edge coloring problem, and introduce a step of topology simplification to degrade the complexity of the problem. Novel policies are proposed to select edges, group edges and color edges. Some results demonstrate the effectiveness of our algorithms and performance gains of network by channel assignment.