We present an effective linear response approach to pump-probe femtosecond coherence spectroscopy in the well-separated pulse limit. The treatment presented here is based on a displaced and squeezed state representation for the nonstationary states induced by an ultrashort pump laser pulse or a chemical reaction. The subsequent response of the system to a delayed probe pulse is modeled using closed form nonstationary linear response functions, valid for a multimode vibronically coupled system at arbitrary temperature. When pump-probe signals are simulated using the linear response functions, with the mean nuclear positions and momenta obtained from a rigorous moment analysis of the pump induced (doorway) state, the signals are found to be in excellent agreement with the conventional third-order response approach. The key advantages offered by the moment analysis-based linear response approach include a clear physical interpretation of the amplitude and phase of oscillatory pump-probe signals, a dramatic improvement in computation times, a direct connection between pump-probe signals and equilibrium absorption and dispersion lineshapes, and the ability to incorporate coherence associated with rapid nonradiative surface crossing. We demonstrate these aspects using numerical simulations, and also apply the present approach to the interpretation of experimental amplitude and phase measurements on reactive and nonreactive samples of the heme protein myoglobin. The role played by inhomogeneous broadening in the observed amplitude and phase profiles is discussed in detail. We also investigate overtone signals in the context of reaction driven coherent motion.