Compression systems of real signals (images, video, audio) generate sources of information with different levels of priority which are then encoded with variable length codes (VLC). This paper addresses the issue of robust transmission of such VLC encoded heterogeneous sources over error-prone channels. VLCs are very sensitive to channel noise: when some bits are altered, synchronization losses can occur at the receiver. This paper describes a new family of codes, called multiplexed codes, that confine the de-synchronization phenomenon to low priority data while asymptotically reaching the entropy bound for both (low and high priority) sources. The idea consists in creating fixed length codes for high priority information and in using the inherent redundancy to describe low priority data, hence the name multiplexed codes. Theoretical and simulation results reveal a very high error resilience at almost no cost in compression efficiency.