The phase separation behavior of bisphenol-A-polycarbonate (PC), dissolved in N-methyl-2-pyrrolidone and dichloromethane solvents in coagulant water, was studied by the cloud point method. The respective cloud point data were determined by titration against water at room temperature and the characteristic binodal curves for the ternary systems were plotted. Further, the physical properties such as viscosity, refractive index, and density of the solution were measured. The critical polymer concentrations were determined from the viscosity measurements. PC/NMP and PC/DCM membranes were fabricated by the dry-wet phase inversion technique and characterized for their morphology, structure, and thermal stability using field emission scanning electron microscopy, Fourier transform infrared spectroscopy, and thermogravimetric analysis, respectively. The membranes’ performances were tested for their permeance to CO2, CH4, and N2 gases at 24 ± 0.5 °C with varying feed pressures from 2 to 10 bar. The PC/DCM membranes appeared to be asymmetric dense membrane types with appreciable thermal stability, whereas the PC/NMP membranes were observed to be asymmetric with porous structures exhibiting 4.18% and 9.17% decrease in the initial and maximum degradation temperatures, respectively. The ideal CO2/N2 and CO2/CH4 selectivities of the PC/NMP membrane decreased with the increase in feed pressures, while for the PC/DCM membrane, the average ideal CO2/N2 and CO2/CH4 selectivities were found to be 25.1 ± 0.8 and 21.1 ± 0.6, respectively. Therefore, the PC/DCM membranes with dense morphologies are appropriate for gas separation applications.