We present a new model for the study of spin-orbit coupling in interacting quasi-one-dimensional systems and solve it exactly to find the spectral properties of such systems. We show that the combination of spin-orbit coupling and electron-electron interactions results in the replacement of separate spin and charge excitations with two new kinds of bosonic mixed-spin-charge excitation, and a characteristic modification of the spectral function and single-particle density of states. Our results show how manipulation of the spin-orbit coupling, with external electric fields, can be used for the experimental determination of microscopic interaction parameters in quantum wires.