Permittivity depends on the electric field intensity in a nonlinear material, and it changes with the incident intensity of the electromagnetic wave. This phenomenon leads to the occurrence of optical bistability. The optical bistable threshold value depends on the localized degree of electromagnetic field in the nonlinear material, and the stronger the localized field, the lower the threshold value is. However, the loss of material is one of the important factors influencing the strength of the local field. It is commonly believed that the loss is not conducible to reducing the threshold value because increased loss can weaken the localized degree of fields. For the lossy single-negative metamaterial, the transmission is nonmonotonic as the loss varies. That is to say, the transmission first decreases and then increases in the lossy single-negative metamaterial. Therefore, the nonlinear transmission in the lossy single-negative metamaterial may lead to novel physical phenomena. Permeability-negative material and permittivity-negative material are two kinds of different single-negative metamaterials. In this paper, the optical bistable phenomena in the heterostructure of permeability-negative material and permittivity-negative material are studied by using the transfer matrix method. Here, the permittivity-negative material is nonlinear material. The results show that the optical bistable threshold value first increases and then falls down as the loss increases. The variance of the localized electromagnetic field at the interface between the permeability-negative layer and the permittivity-negative layer at the discussed frequency is discussed in the present paper to understand the nonmonotonic phenomenon. Further studies indicate that the nonmonotonic localized electromagnetic field is also presented at the interface between the permeability-negative layer and permittivity-negative layer. That is to say, the enhancement of the localized field can be obtained when the loss is increased, which results in the nonmonotonic optical bistable threshold value in the heterosturcture composed of the single-negative metamaterials. In the final analysis, the abnormal phenomenon is induced by the loss in the single-negative metamaterial, which is the special property of single-negative metamaterial.