We present a parallel time‐marching scheme for coupled parabolic‐hyperbolic problems, as a prototype of fluid‐structure interaction problems involving a linear structure and a viscous fluid. No linearity assumption is made on the parabolic side. The classical Parareal scheme is applied to the parabolic part, while the modified algorithm proposed by Farhat et al. [1] is applied to the hyperbolic part. This hybrid Parareal treatment relies on the partitioned formulation of the coupled propagator. Numerical evidence shows that the resulting scheme is stable for a wide range of physical and discretization parameters.