Fibers consisting of a rigid rod polymer and thermoset resin matrices were prepared. Poly{(benzo-[1,2-d : 5,4-d’]bisoxazole-2,6-diyl)-1,4-phenylene} (PBO) in polyphosphoric acid (PPA) was blended with isophthaloyl bis-4-benzocyclobutene (1) or 2,6-bis-4-benzocyclobutene benzo[1,2-d : 5,4-d’]bisoxazole (2), and fibers were spun from these dopes. As-spun fibers that did not show phase segregation between the two components as examined with an optical microscope, were soluble in methanesulfonic acid (MSA). After heat treatment, the fibers swelled but did not dissolve in MSA. A fiber cross section of heat-treated PBO-1 fiber showed well-dispersed benzocyclobutene polymer domains of 200-500 Angstrom by transmission electron microscopy (TEM). Films cast from MSA solutions of PBO and 2 were homogeneous, and TEM of heat-treated fiber showed only one phase. A molecular composite fiber was made. Some of these fibers showed 20-30% improvement in compressive strength over unmodified PBO fiber.