We report on the selective imaging of different director fields in a biaxial smectic A (SmAb) liquid crystal using Fluorescence Confocal Polarizing Microscopy (FCPM) and Polarizing Microscopy (PM). The patterns of two directors, namely the director n(a) perpendicular to the lamellae and the director n(b) in their planes are visualized by doping the liquid crystal with two fluorescent dyes with different orientation of the transition dipoles with respect to the lamellar matrix. The properties of defects such as disclinations and focal conic domains (FCDs) are consistent with the non-polar D2h-symmetry of the SmA(b) mesophase in the studied mixture of bent-core and rod-like molecules: (1) majority of defects in the director n(b) are half-integer "+/-1/2" disclinations; (2) the integer-strength "+/-1" defects tend to split into the "+/-1/2" disclinations. We compare the vertical cross-sections of the "+/-1" disclinations in the field in SmA(b) and uniaxial nematic samples. In SmA(b), the "+/-1" disclinations do not escape into the third dimension, while in the nematic samples with Schlieren textures they do despite the surface anchoring at the plates; the experimentally determined director field around the escaped disclination capped by a pair of surface point defects--boojums matches the one predicted recently [C. Chiccoli et al., Phys. Rev. E 66, 030701 (2002)]. The FCD structure in SmA(b) is similar to that in SmA and SmC in terms of the normal to the layers but differs significantly in terms of the director n(b) field parallel to the smectic layers. The FCDs in SmA(b) can be associated with topologically non-trivial configurations of n(b) in the surrounding matrix that are equivalent to the disclination lines.