Magnetoimpedance (MI) biosensors for the detection of in-tissue incorporated magnetic nanoparticles are a subject of special interest. The possibility of the detection of the ferrogel samples mimicking the natural tissues with nanoparticles was proven previously for symmetric MI thin-film multilayers. In this work, in order to describe the MI effect in non-symmetric multilayered elements covered by ferrogel layer we propose an electromagnetic model based on a solution of the 4Maxwell equations. The approach is based on the previous calculations of the distribution of electromagnetic fields in the non-symmetric multilayers further developed for the case of the ferrogel covering. The role of the asymmetry of the film on the MI response of the multilayer-ferrogel structure is analyzed in the details. The MI field and frequency dependences, the concentration dependences of the MI for fixed frequencies and the frequency dependence of the concentration sensitivities are obtained for the detection process by both symmetric and non-symmetric MI structures.