To enable the smart grid concept, it is fundamental to consider the in-home/building context where, beside the conventional home networking services, home automation and smart energy management services have to be offered. In this paper, we consider the in-home/building scenario, for which we propose a convergent network architecture to enhance the performance of the narrowband power line communication (PLC) G3-PLC technology through its integration with an Ethernet-based network. To this end, we define the protocols characterizing the network modules, namely, switches and routers, which allow for integrating the G3-PLC with Ethernet devices. Since Ethernet represents a convergent standard for many communication devices, by adding this functionality to G3-PLC, interconnectivity with other heterogeneous nodes can be offered. Furthermore, since the G3-PLC medium access control layer is based on a carrier sense multiple access scheme, its performance decreases when the number of network nodes contending for the channel increases. Therefore, we evaluate the network performance when an optimized time division multiple access scheme is adopted. The proposed convergent network architecture has been implemented in the OMNeT++ network simulator.