Given a placement of wireless multi-radio nodes in space and a traffic demand between pairs of nodes, can these traffic demands be supported by the resulting network? The key issue in this setting is the wireless interference between neighbouring nodes using the same channel, including self-interference along multi-hop paths. We extend previous work addressing this problem taking into consideration the availability of multiple channels. As such, this paper presents a generic model for sustainable network load in a multi-hop multi-channel setting and recasts this model in a multicommodity flow problem with interference constraints. A theorem is stated which gives a necessary and sufficient condition for the feasibility of this multicommodity flow problem. From this theorem an upper bound is derived for the throughput that can be achieved by the network, which is illustrated by examples. We indicate how the results can be used as a basis for a channel allocating algorithm.