Strength and strain sensitivity of a thin polymer-ceramic coating in the form of a nanoporous anodic aluminum oxide impregnated with a piezoelectric polymer are studied. The coating is considered as a unidirectionally reinforced composite containing cylindrical polymer fibers oriented perpendicular to the coating surface. A three-phase micromechanical model of the specified material is proposed and the stress-strain state of the coating under the influence of uniformly distributed pressure is analyzed. As a result of solving the related problem of electroelasticity, calculated estimates of the specific piezoelectric sensitivity of the coating used as a pressure sensor and the maximum allowable pressure were obtained according to the strength criteria of the ceramic matrix and the plastic flow of the polymer filler. The article shows dependences of the indicated parameters on the volumetric content of the polymer for the coating, adhesively bonded to a non-deformable foundation and freely (without friction) lying on the foundation. At low volume content of polymer, the strength loss of coating is caused by local failure of matrix. At high filler content the transition of polymer into plastic state precedes to the beginning of matrix failure. After increasing the filler content above 80 % the value of maximal pressure according to yield criteria for polymer filler scarcely changes.