Miscibility characteristics of poly-p-phenylene benzobisoxazole (PPBO)/amorphous nylon (AN) molecular composites were studied by means of differential scanning calorimetry (DSC), dielectric relaxation, wide-angle x-ray diffraction (WAXD), and light scattering. The solution-mixed PPBO/AN exhibited a systematic movement of a single glass transition temperature (Tg) with composition in DSC and dielectric measurements, implying an entrapped single phase of the molecular composites. In the WAXD studies of the 50/50 mixture, two very weak reflection peaks of the PPBO phase and a small amorphous halo of AN were discerned. Light scattering studies showed no detectable level of orientation fluctuations. Upon heating, thermally induced phase separation occurred, with a cloud point phase diagram reminiscent of a lower critical solution temperature (LCST). As typical for entrapped single-phase blends, the phase diagram of LCP blends is irreversible. Nevertheless, several temperature jump experiments were undertaken from ambient temperature to a two-phase temperature region in order to gain further insight into the nonequilibrium behavior. The time-evolution of scattering profiles was analyzed in the context of nonlinear theories and dynamical scaling laws. The kinetic exponent of the phase growth was found to be consistent with the prediction of cluster dynamics proposed by Binder and Stauffer.