We study lossy communication of correlated sources over a multiple access channel. In particular, we provide a joint source-channel coding scheme for transmitting correlated sources with decoder side information, and study the conditions under which separate source and channel coding is optimal. For the latter, the encoders and/or the decoder have access to a common observation conditioned on which the two sources are independent. By establishing necessary and sufficient conditions, we show the optimality of separation when the encoders and the decoder both have access to the common observation. We also demonstrate that separation is optimal when only the encoders have access to the common observation whose lossless recovery is required at the decoder. As a special case, we study separation for sources with a common part. Our results indicate that side information can have significant impact on the optimality of source-channel separation in lossy transmission.