This work presents a Green's function approach, originally implemented in graphene with well-defined edges, to the surface of a strong 3D Topological Insulator (TI) with a sequence of proximitized superconducting (S) and ferromagnetic (F) surfaces. This consists of the derivation of the Green's functions for each region by the asymptotic solutions method, and their coupling by a tight-binding Hamiltonian with the Dyson equation to obtain the full Green's functions of the system. These functions allow the direct calculation of the momentum-resolved spectral density of states, the identification of subgap interface states, and the derivation of the differential conductance for a wide variety of configurations of the junctions. We illustrate the application of this method for some simple systems with two and three regions, finding the characteristic chiral state of the Quantum Anomalous Hall Effect (QAHE) at the NF interfaces, and chiral Majorana modes at the NS interfaces. Finally, we discuss some geometrical effects present in three-region junctions such as weak Fabry-P\'erot resonances and Andreev bound states.