In the present work, some optical properties related to intersubband transitions in finite depth asymmetric hyperbolic-type quantum wells are theoretically investigated. The use of a hyperbolic potential configuration would account for the actual – non abrupt – confinement potential in the heterostructure, in the case of modulated growing or when compositional diffusion across the interfaces turns out to be relevant. In the investigation, the presence of externally applied electromagnetic fields is considered. Electron conduction band states are determined within the parabolic band an effective mass approximation. With the electronic structure information at hand, it is possible to evaluate the linear and third-order nonlinear light absorption and relative refractive index change coefficients, from expression arising in the framework of the compact density matrix approach. According to the theoretical outcome, it is found that: (i) There is a significant influence of the structural configuration on the magnitude and resonant peak position of the total optical coefficients. (ii) Under the effect of increasing external electric and magnetic fields, the peak energy positions are shifted towards higher values, whereas their amplitude decrease for the optical absorption case, and that of the refractive index relative variation is reduced. From these results it can be concluded that both the modification of the confinement profile and the presence of electric and/or magnetic fields are suitable tool to control the optical response of asymmetric hyperbolic-type semiconductor quantum wells. © 2020 Elsevier B.V.