Constrained multiobjective optimization problems (CMOPs) are challenging because of the difficulty in handling both multiple objectives and constraints. While some evolutionary algorithms have demonstrated high performance on most CMOPs, they exhibit bad convergence or diversity performance on CMOPs with small feasible regions. To remedy this issue, this article proposes a coevolutionary framework for constrained multiobjective optimization, which solves a complex CMOP assisted by a simple helper problem. The proposed framework evolves one population to solve the original CMOP and evolves another population to solve a helper problem derived from the original one. While the two populations are evolved by the same optimizer separately, the assistance in solving the original CMOP is achieved by sharing useful information between the two populations. In the experiments, the proposed framework is compared to several state-of-the-art algorithms tailored for CMOPs. High competitiveness of the proposed framework is demonstrated by applying it to 47 benchmark CMOPs and the vehicle routing problem with time windows.