The branched copolymer–substrate system we investigate in this study represents a hybrid interface where the central monomer of a flexible polymer chain is grafted to a solid substrate. The presence of two subchains extending from the grafted monomer introduces additional structural complexity compared to end-grafted polymers. Different energy scales for inter-chain and intrachain monomer-monomer interactions cause even more heterogeneity. We employ the microcanonical inflection-point analysis method to study the phase behavior of a coarse-grained model for this system. For this purpose, extensive replica-exchange Monte Carlo simulations of the model were performed. Microcanonical statistical analyses of the entropy and its derivatives, combined with a detailed analysis of structural phase parameters, reveal distinct transitions between expanded, desorbed/adsorbed globular, and crystalline phases. This combined analysis uncovers the emergence of stable composite aggregates in several structural phases.