We report a theoretical calculation of the strain-mediated magnetocapacitance of ferroelectric-ferromagnetic heterostructures. Our nonlinear theory predicts that this magnetocapacitance strongly depends on the strain state of a ferroelectric constituent. For multiferroic hybrids comprising a BaTiO3 or Pb(Zr0.5Ti0.5)O3 film and a FeBSiC, Terfenol-D, or FeGa substrate, the magnetocapacitive coefficient generally has a giant value ∼10−4 Oe−1. Remarkably, its magnitude further increases drastically near the strain-induced phase transition at which the out-of-plane polarization appears in the ferroelectric film. As a result, the magnetocapacitance of hybrids including Terfenol-D may exceed 100% already at the magnetic field of about 600 Oe. These theoretical results provide guidelines for the fabrication of multiferroic heterostructures exhibiting a strong magnetodielectric effect.