Full-duplex self-backhauling is promising to provide cost-effective and flexible backhaul connectivity for ultra-dense wireless networks, but also poses a great challenge to resource management between the access and backhaul links. In this paper, we propose a user-centric joint access-backhaul transmission framework for full-duplex self-backhauled wireless networks. In the access link, user-centric clustering is adopted so that each user is cooperatively served by multiple small base stations (SBSs). In the backhaul link, user-centric multicast transmission is proposed so that each user's message is treated as a common message and multicast to its serving SBS cluster. We first formulate an optimization problem to maximize the network weighted sum rate through joint access-backhaul beamforming and SBS clustering when global channel state information (CSI) is available. This problem is efficiently solved via the successive lower-bound maximization approach with a novel approximate objective function and the iterative link removal technique. We then extend the study to the stochastic joint access-backhaul beamforming optimization with partial CSI. Simulation results demonstrate the effectiveness of the proposed algorithms for both full CSI and partial CSI scenarios. They also show that the transmission design with partial CSI can greatly reduce the CSI overhead with little performance degradation.