The capping effect in magnetic double-film systems has been studied theoretically by means of a variational method for magnetic energies in a continuum model. The coercive force of the double-film system is given explicitly in terms of the magnetic constants of the two films. A field Hcap is defined regarding the exchange coupling between the films as an effective Zeeman energy, and it is found that Hcap enhances the external field in recording processes. Since Hcap felt by the magnetization in the recording film is localized near the interface, a domino phenomenon of magnetization in the recording film is expected. It is triggered by accidental nucleations at the interface, as part of the dynamic process of recording. A phase transition between different alignments of magnetization is found when the thickness of the capping film is varied and the mechanism of this phase transition is clarified. The critical point is derived analytically which gives also the minimal thickness of the capping film that shows the capping effect. It is found that the critical behavior of Hcap in the vicinity of the minimal thickness is characterized by an exponent β=1. The capping effect at large thickness limit is also discussed.