In a network with a shared communication channel having limited transmission range, topology-transparent protocols support communication among neighbouring nodes, even when the only information a node has about its neighbourhood is the maximum number of active transmitters within range. Cover-free families provide the underlying schedules to allocate time slots for transmission to a node so as to maximize the number of active transmitters permitted while guaranteeing at least one collision-free slot. Scheduling can reduce contention by limiting the number of active transmitters. In this paper we generalize topology-transparent schemes to communication on multiple channels, in which each node is equipped with many radio interfaces. The goal is to ensure that for every transmitter and every receiver, some channel is shared by them but not interfered with by any other set of potential transmitters, provided that that set is not too large. This requirement is met by a generalized cover-free family.