By mimicking broken mirror symmetry of naturally existing chiral materials, and exploiting even stronger magnetoelectric coupling, large optical activity has been realized in chiral metamaterials over the past decade. Nevertheless, most of chiral metamaterials demonstrated so far exhibit highly dispersive optical activity due to their resonant response, which inevitably leads to a narrow operating bandwidth in terms of the optical rotatory power as well as the transmission. Herein, conditions for possessing nondispersive optical activity are derived based on a Lagrangian model for general bilayer chiral metamaterials, and the validity is experimentally confirmed in a microwave regime. It is shown that large nondispersive optical activity can be realized in bilayer chiral metamaterials where metallic apertures are arranged in each layer with high-rotational symmetry and the off-diagonal terms of the magnetic interlayer coupling tensor are nonzero while the electric counterparts are eliminated. In stark contrast to most previous chiral metamaterials, a nonzero constant polarization rotation angle is observed at the quasi-static limit, which manifests the unique nonresonant characteristic of the proposed magnetically coupled bilayer chiral metamaterials. In addition to the geometrical controllability, the amount of polarization rotation and transmission bandwidth can be further increased by stacking magnetically coupled bilayer chiral metamaterials.