This paper tackles a non-orthogonal multiplexing (NOM)-based realization of broadcast-unicast overlay transmission in cloud-radio access networks (C-RANs). In particular, fronthaul compression and precoding are jointly optimized to maximize the throughput in the considered network. The problem further optimizing the power allocation between broadcast and unicast signals is addressed as well. The algorithmic solutions are obtained by means of majorization minimization (MM)-type difference-of-convex (DC) programming. Moreover, the proposed solutions are further extended to cope with the uncertainty of channel state information (CSI) to enable robust transmission. Computer simulations are performed to verify that the proposed scheme attains substantial achievable rate gain over the conventional decentralized precoding in entire parameter regions considered.