Two-dimensional infrared (2DIR) spectroscopy is widely used to study molecular dynamics but it is typically restricted to optically thick samples and modest spectral resolution. The recently proposed technique of cavity-enhanced 2D spectroscopy using frequency combs and developments in multi-comb spectroscopy can lift these restrictions, demonstrating the need for rigorous and quantitative treatment of rotationally-resolved, polarization-dependent third-order response of gas-phase samples. This article provides such description using density-matrix, time-dependent perturbation theory and angular momentum algebra techniques. We describe the band and branch structure of 2D spectra, decompose the molecular response into polarization-dependence classes, use this decomposition to derive and explain special polarization conditions and relate the liquid-phase polarization conditions to gas-phase ones. Furthermore, we discuss the rotational coherence dynamics during waiting time.