A theoretical study on the effect of spontaneous polarization screening on the dielectric response of ferroelectric films with 180 degrees domains going through the film thickness (through-domains) is presented. It has been shown by several researchers that the dielectric response of ferroelectrics is always deteriorated (e.g. due to electricfield, mechanical stress, or lattice imperfections) in the thin electrode-adjacent passive regions. As a result, these regions behave as a low dielectric material reducing the total dielectric response of the ferroelectric capacitor. This "depolarizing" effect can be modeled by a low-dielectric layer between the ferroelectric and the electrode. The strong electric field in the dielectric layer can induce free charge injection from the electrode to the ferroelectric-dielectric layer interface. We study how these free charges affect the dielectric response of the ferroelectric capacitor with through-domains. We found that their presence strongly influences the domain wall contribution to permittivity of the ferroelectric. This effect is controlled to a great extent by the domain wall thickness.