We consider transmission of stationary ergodic sources over non-ergodic composite channels with channel state information at the receiver (CSIR). Previously we introduced alternative capacity definitions to Shannon capacity, including outage and expected capacity. These generalized definitions relax the constraint of Shannon capacity that all transmitted information must be decoded at the receiver. In this work alternative endto-end distortion metrics such as outage and expected distortion are introduced to relax the constraint that a single distortion level has to be maintained for all channel states. Through the example of transmission of a Gaussian source over a slow-fading Gaussian channel, we illustrate that the end-to-end distortion metrics dictate whether the source and channel coding can be separated for a communication system. We also show that the source and channel need to exchange information through an appropriate interface to facilitate separate encoding and decoding.