Abstract Collisionless shocks and plasma turbulence are crucial ingredients for a broad range of astrophysical systems. The shock–turbulence interaction, and in particular the transmission of fully developed turbulence across the quasi-perpendicular Earth’s bow shock, is here addressed using a combination of spacecraft observations and local numerical simulations. An alignment between the Wind (upstream) and Magnetospheric Multiscale (downstream) spacecraft is used to study the transmission of turbulent structures across the shock, revealing an increase of their magnetic helicity content in its downstream. Local kinetic simulations, in which the dynamics of turbulent structures are followed through their transmission across a perpendicular shock, confirm this scenario, revealing that the observed magnetic helicity increase is associated with the compression of turbulent structures at the shock front.