A temporal network is a dynamic graph where every edge is assigned an integer time label that indicates at which discrete time step the edge is available. We consider the problem of hierarchically decomposing the network and introduce an edge-based decomposition framework that unifies the core and truss decompositions for temporal networks while allowing us to consider the network's temporal dimension. Based on our new framework, we introduce the $(k,Δ)$-core and $(k,Δ)$-truss decompositions, which are generalizations of the classic $k$-core and $k$-truss decompositions for multigraphs. Moreover, we show how $(k,Δ)$-cores and $(k,Δ)$-trusses can be efficiently further decomposed to obtain spatially and temporally connected components. We evaluate the characteristics of our new decompositions and the efficiency of our algorithms. Moreover, we demonstrate how our $(k,Δ)$-decompositions can be applied to analyze malicious content in a Twitter network to obtain insights that state-of-the-art baselines cannot obtain.