Hybrid 2D hard-soft composites have been fabricated by combining soft (Co73Si27) and hard (NdCo5) magnetic materials with in-plane and out-of-plane magnetic anisotropies, respectively. They have been microstructured in a square lattice of CoSi anti-dots with NdCo dots within the holes. The magnetic properties of the dots allow us to introduce a magnetostatic stray field that can be controlled in direction and sense by their last saturating magnetic field. The magnetostatic interactions between dot and anti-dot layers induce a completely tunable exchange bias-like shift in the system's hysteresis loops. Two different regimes for this shift are present depending on the lattice parameter of the microstructures. For large parameters, dipolar magnetostatic decay is observed, while for the smaller one, the interaction between the adjacent anti-dot's characteristic closure domain structures enhances the exchange bias-like effect as clarified by micromagnetic simulations.