I agree with Dr. Jehan. I can only add that thermodynamic parameters along with the chemical parameters determine compatibility. Solubility parameters can also help. Melt blending is done mostly by extruder. You have to play with screw zone lengths, temperature and addition point etc. If there is good secondary interaction between the two the blending is improved. If all fail use a compatibilizer. Some times nanoparticles help.
Beside the observation of the micro-structure and the investigation of the thermal properties, you can also determine the compatibility of polymers by using tensile test. if your polymers have a good compatibility, they will have a good miscibility or a good interface. The mechanical properties of the polymer composites such as the rigidity or the elongation at break will be improved depended on the polymer matrix and reinforced polymer.