In situ interfacial rheology and numerical simulations are used to investigate microgel monolayers in a wide range of packing fractions, xi(2D). The heterogeneous particle compressibility determines two flow regimes characterized by distinct master curves. To mimic the microgel architecture and reproduce experiments, an interaction potential combining a soft shoulder with the Hertzian model is introduced. In contrast to bulk conditions, the elastic moduli vary nonmonotonically with xi(2D) at the interface, confirming long-sought predictions of reentrant behavior for Hertzian-like systems.