With the rapid increase in the number of technologies aimed at observing electric activity inside the brain, scientists have felt the urge to create proper links between intracellular- and extracellular-based experimental approaches. Biophysical models at both physical scales have been formalized under assumptions that impede the creation of such links. In this work, we address this issue by proposing a multicompartment model that allows the introduction of complex extracellular and intracellular resistivity profiles. This model accounts for the geometrical and electrotonic properties of any type of neuron through the combination of four devices: the integrator, the propagator, the 3D connector, and the collector. In particular, we applied this framework to model the tufted pyramidal cells of layer 5 (PCL5) in the neocortex. Our model was able to reproduce the decay and delay curves of backpropagating action potentials (APs) in this type of cell with better agreement with experimental data. We used the voltage drops of the extracellular resistances at each compartment to approximate the local field potentials generated by a PCL5 located in close proximity to linear microelectrode arrays. Based on the voltage drops produced by backpropagating APs, we were able to estimate the current multipolar moments generated by a PCL5. By adding external current sources in parallel to the extracellular resistances, we were able to create a sensitivity profile of PCL5 to electric current injections from nearby microelectrodes. In our model for PCL5, the kinetics and spatial profile of each ionic current were determined based on a literature survey, and the geometrical properties of these cells were evaluated experimentally. We concluded that the inclusion of the extracellular space in the compartmental models of neurons as an extra electrotonic medium is crucial for the accurate simulation of both the propagation of the electric potentials along the neuronal dendrites and the neuronal reactivity to an electrical stimulation using external microelectrodes.