Two-dimensional (2D) numerical experiments are performed to investigate the flow instabilities and mixing of different nonisothermal counterflowing jets in a passive-mixer. The fluid is modeled as a binary mixture with thermal and solutal buoyancy effects considered through the Boussinesq approximation. The streams are arranged in a thermal and solutal buoyancy aiding configuration. Computations are carried out for three different ratios of the upper jet bulk velocity to the lower jet bulk velocity (VR), namely, VR = 0.5, 1.0, and 2. Within the parametric domain of RiT and RiC defined by region (RiT + RiC) ≤ 3, the instability causing transition from steady to unsteady flow regime is observed for VR = 1 and 2, while no transition is found to occur at VR = 0.5. Using Landau theory, it is established that the transition from steady to unsteady flow regime is a supercritical Hopf bifurcation. A complete regime map identifying the steady and unsteady flow regimes, within the parametric space of this study, is obtained by plotting the neutral curves of RiC and RiT (obtained using Landau theory) for different values of VR. Proper orthogonal decomposition (POD) analysis of the unsteady flows at VR = 1 establishes the presence of standing waves. However, for VR = 2, the presence of degenerate pairs in the POD eigenspectrum ascertains the presence of traveling waves in the unsteady flows. The standing wave unsteady flow mode is found to yield the highest rate of mixing.