We show that the coupling between two ferromagnetic layers separated by a nonmagnetic spacer can be used to control the depinning of domain walls and induce unidirectional domain wall propagation. We investigated CoFeB/Ti/CoFeB trilayers where the easy axis of the magnetization of the top CoFeB layer is out of plane and that of the bottom layer is in plane. Using magneto-optic Kerr effect microscopy, we find that the depinning of a domain wall in the perpendicularly magnetized CoFeB layer is influenced by the orientation of the magnetization of the in-plane layer, which gives rise to a field-driven asymmetric domain expansion. This effect occurs due to the magnetic coupling between the internal magnetization of the domain wall and the magnetization of the in-plane CoFeB layer, which breaks the symmetry of up-down and down-up homochiral Néel domain walls in the perpendicular CoFeB layer. Micromagnetic simulations support these findings by showing that the interlayer coupling either opposes or favors the Dzyaloshinskii-Moriya interaction in the domain wall, thereby generating an imbalance in the depinning fields. This effect also allows for artificially controlling the chirality and dynamics of domain walls in magnetic layers lacking a strong Dzyaloshinskii-Moriya interaction.