The interaction of a two-level dipolar molecule with two laser pulses, where one laser’s frequency is tuned to the energy level separation (pump laser) while the second laser’s frequency is extremely small (probe laser), is investigated. A dipolar molecule is one with a nonzero difference between the permanent dipole moments of the molecular states. As shown previously [A. Brown, Phys. Rev. A 66, 053404 (2002)], the final population transfer between the two levels exhibits a dependence on the carrier-envelope phase of the probe laser. Based on the rotating-wave approximation (RWA), an effective Hamiltonian is derived to account for the basic characteristics of the carrier-envelope phase dependence effect. By analysis of the effective Hamiltonian, scaling properties of the system are found with regard to field strengths, pulse durations, and frequencies. According to these scaling properties, the final-state population transfer can be controlled by varying the carrier-envelope phase of the probe laser field using lasers with weak field strengths (low intensities) and relatively long pulse durations. In order to examine the possible roles of background states, the investigation is extended to a three-level model. It is demonstrated that the carrier-envelope phase effect still persists in a well-defined manner even when neighboring energy levels are present. These results illustrate the potential of utilizing excitation in dipolar molecules as a means of measuring the carrier-envelope phase of a laser pulse or if one can manipulate the carrier envelope phase, as a method of controlling population transfer in dipolar molecules. The results also suggest that the carrier-envelope phases must be taken into account properly when performing calculations involving pump-probe excitation schemes with laser frequencies which differ widely in magnitude.