Two-dimensional spectroscopy (2DS) offers significant advantages in terms of high temporal and frequency resolutions and signal-to-noise ratio. Until now, the response-function (RF) formalism has been the prevalent theoretical description. In this study, we compare the non-Hermitian Hamiltonian (NHH) method with the RF formalism in a three-level system with a constant control field. We obtain the signals from both approaches and compare their population dynamics and 2DS. We propose the quasi-Green function for the NHH method, which allows all possible Liouville paths to be inferred. Although the NHH method overestimates relaxations, it also provides a more comprehensive description. Our results demonstrate that the NHH method is more suitable than the RF formalism for investigating the systems that are either dissipative or complex via the 2DS.