We consider the problem of sending a Gaussian source over a fading channel with Gaussian interference known to the transmitter. We study joint source-channel coding schemes for the case of unequal bandwidth between the source and the channel and when the source and the interference are correlated. An outer bound on the system's distortion is first derived by assuming additional information at the decoder side. We then propose layered coding schemes based on proper combination of power splitting, bandwidth splitting, Wyner-Ziv and hybrid coding. More precisely, a hybrid layer, that uses the source and the interference, is concatenated (superimposed) with a purely digital layer to achieve bandwidth expansion (reduction). The achievable (square error) distortion region of these schemes under matched and mismatched noise levels is then analyzed. Numerical results show that the proposed schemes perform close to the best derived bound and to be resilient to channel noise mismatch. As an application of the proposed schemes, we derive both inner and outer bounds on the source-channel-state distortion region for the fading channel with correlated interference; the receiver, in this case, aims to jointly estimate both the source signal as well as the channel-state (interference).