Novel two-dimensional vibrational spectroscopic methods utilizing an infrared (IR) and two off-resonant optical pulses are theoretically studied. Unlike the coherent two-dimensional Raman or IR spectroscopies, the two successive vibrational coherence states are generated by an interaction with IR field as well as two interactions with off-resonant optical fields. Then, the emitted IR signal field is detected. The corresponding nonlinear response functions and their two-dimensional Fourier transforms are obtained in the analytical forms. It is shown that these methods are especially useful in studying the mode couplings and dynamics of only those vibrational modes that are both IR- and Raman active. A few numerically calculated 2D spectra are presented and compared with other types of coherent two-dimensional vibrational spectroscopies, such as coherent 2D Raman scattering or IR spectroscopies.