This work considers the downlink of a cloud radio access network (C-RAN) in which a baseband processing unit (BBU) sends independent messages to multiple user equipments (UEs) by controlling a set of remote radio heads (RRHs) which are connected to the BBU via finite-capacity fronthaul links. In standard C-RAN systems, it is prescribed that the fronthaul links are used in a soft-transfer mode whereby quantized signals of the baseband signals, that encode the UEs' messages, are transferred on the fronthaul links. Although this approach is advantageous in a sense that the RRHs do not need to have baseband signal processing functionalities, it has been reported that one can achieve better performance with hard-transfer fronthauling scheme, whereby the fronthaul links are used to transfer hard information of the UEs' messages, particularly when the fronthaul links have relatively large capacity. This work proposes a unified scheme that leverages hybrid soft -transfer and hard-transfer fronthauling strategies. This is enabled by a superposition coding where each UE message is split into two submessages that are delivered to the UEs by means of soft-transfer or hard-transfer schemes. Some numerical results are provided to confirm the advantages of the proposed hybrid scheme.