The hybrid approach coupling Statistical Energy Analysis (SEA) and the finite element method has become a prominent technique for analysing structures under steady-state loads in the ‘mid-frequency’ range where some components behave in a deterministic manner with low modal density and others in a statistical manner with high modal density and statistical overlap. In this paper, the method is extended from its current steady-state capability to provide calculation of structural responses under impulsive and time-varying loads. Similar to the steady-state method, a system is split into deterministic components that are modelled using the finite element approach and statistical components that are modelled as SEA subsystems. An evolutionary spectrum approach based on the Priestley description of random processes is applied to model the response of both the SEA and deterministic components which are coupled by considering a power balance between the SEA subsystems. The diffuse field reciprocity relationship that relates the reverberant forces generated by a subsystem to the energy within it is explored under transient conditions where it is found that it can be important to account for the build-up of a reverberant field following an impulse. Results from the method are compared against finite element simulations for a system of plates coupled by a beam and it is found to generate predictions with the accuracy expected of an SEA-based method, although deterministic oscillations of the deterministic system at early times are not accounted for.