This paper presents a strategy for multi-modal trip planning integrating the management of fully electric vehicle range and charging services along the trip. The network graph is modelled as the superposition of layers representing different transportation means and charging infrastructure, putting in evidence the interaction between the transportation and electricity distribution grids. The presence of energy constraints on the network nodes implies to formalize the trip planning problem as a resource constrained shortest path problem, and solve it through an ad-hoc decomposition strategy. The proposed approach is validated through the simulation of realistic test cases, showing its effectiveness and potential in satisfying complex user preferences, mitigating drivers perception about limited vehicle range and availability of charging infrastructure, smoothing the impact of massive fully electric vehicle charging on distribution grids.