Electronic devices and equipment may communicate over a wired communications path. The wired communications path may include one or more wires and may be associated with a headphone cable. Data may be conveyed in the form of a digital data stream containing multiple traffic channels. The digital data stream may include superframes, each of which has multiple frames of data. The frames of data may each contain a number of data slots. Some of the slots in a superframe may be used exclusively by a particular one of the traffic channels. Boundary slots may be shared between traffic channels. Data interface circuitry may implement a data dispersion algorithm that determines the pattern in which data from each traffic channel is distributed within each boundary slot. Transmitting data interface circuitry may merge traffic channels into a single data stream. Receiving data interface circuitry may reconstruct the traffic channels.