A pseudoclassical model for P,T-invariant system of topologically massive U(1) gauge fields is analyzed. The model demonstrates a nontrivial relationship between continuous and discrete symmetries and reveals a phenomenon of ``classical quantization''. It allows one to identify SU(1,1) symmetry and S(2,1) supersymmetry as hidden symmetries of the corresponding quantum system. We show this P,T-invariant quantum system realizes an irreducible representation of a non-standard super-extension of the (2+1)-dimensional Poincaré group.