The classical problem of a two-level quantum system coupled to a bath and coherently driven may be treated using various approaches. Analyzing it using the common secular approximation in the lab frame (as usually done in the context of atomic physics) or in the rotating frame (prevailing in, e.g., the treatment of solid-state qubits) may yield different results. We show how to bridge between these two approaches by working in the rotating frame but not employing the secular approximation. The resulting master equations were further generalized to account for the frequency-dependence of the bath density of states and the possibility of longitudinal coupling between the bath and the two-level system. Using these equations we find the resulting dynamics and steady state of the density matrix, as well as the steady-state correlation functions, and in particular --- the photoluminescence spectrum. While in the appropriate limits we recover the results of the more traditional approaches, in the general case we find new features, such as population inversion and asymmetric Mollow triplet spectrum.