We consider a cache-aided communications system in which a transmitter communicates with many receivers over an erasure broadcast channel. The system serves as a basic model for communicating on-demand content during periods of high network congestion, where some content can be pre-placed in local caches near the receivers. We formulate the cache-aided communications problem as a joint cache-channel coding problem, and characterise some information-theoretic tradeoffs between reliable communications rates and cache sizes. We show that if the receivers experience different channel qualities, then using unequal cache sizes and joint cache-channel coding improves system efficiency.