A vibronic theory of unpolarized infrared absorption and vibrational circular dichroism (VCD) is presented that is valid in the limit of vibrational resonance with low-lying electronic states (LLESs). The theory is developed within the complete adiabatic vibronic coupling formalism that describes both the correlation of electron density to nuclear positions and the correlation of electron current density to nuclear velocities. It is found that additional terms contribute to the electric-dipole and magnetic-dipole transition moments that become zero in the limit where all excited electronic states in the molecule are much higher in energy relative to fundamental vibrational transitions. Two correction terms appear that are extensions of the lowest-order non-Born-Oppenheimer expansion term when vibronic detail is included in the energy denominators. One term is a resonance term with respect to the energy difference between the electronic and vibrational transitions, and the other is a nonresonance term. Under the assumption that vibrational sublevels in LLES are not significantly changed from those in the ground electronic state, the two correction terms can be reduced to a simple frequency-dependent factor that becomes unity in the limit that electronic-state transitions are much higher than vibrational transition energies. The theory is applied to the case of transitions to LLESs that are electric-dipole forbidden and magnetic-dipole allowed, and the relation of these expressions to recent experimental results of VCD enhanced by such LLESs is discussed.