A recently proposed collisional time-correlation function method for resonance laser-target interactions in molecular targets is modified and extended to include time-delayed multiphoton processes in the dynamics. The explicitly time-dependent laser and target dynamics in this method is separated into laser electric field correlation functions, also know as Glauber field correlation functions, are evaluated in a continuum mode description of photon number representation for both resonance and time-delayed multiphoton processes. We show that such a description allows for the incorporation of laser pulse shape and phase coherence in the formalism, while the laser-target interaction dynamics is still described similarly to the resonance single- and multiphoton processes. As an example, the transition rates for a two-photon Gaussian pump-probe dynamics are derived in which we show that the phase coherence between the Gaussian pump and probe pulses can be incorporated and controlled through a single delay-time-dependent parameter.