Hybrid AC/DC networks are an effective solution for future power systems, due to their ability to combine advantages of both AC and DC networks. However, they bring new technological challenges, one key area being the control of such a network. The network, and especially the interlinking converter (ILC), must be controlled to ensure that the DC and AC subsystems coordinate to stabilize the network and allocate power appropriately. This is an area which has attracted considerable recent interest due to the non-triviality of the control design. One promising tool is passivity theory which allows the derivation of decentralized conditions through which the stability of the network can be guaranteed. This paper investigates the application of a passivity framework to AC/DC grids, using a typical lossless line assumption. By ensuring that an appropriately formulated passivity condition is satisfied by the AC and DC buses, and the interlinking converter, the stability of the interconnection can be guaranteed. We also discuss how the ILC controller may be designed to achieve an appropriate power allocation between AC and DC sources. Simulation results demonstrate that the proposed ILC control design regulates the frequency and voltages of the hybrid AC/DC network with a stable operation maintained.