This paper investigates the symmetry of polarimetric scattering and emission coefficients of media with reflection symmetry. A reflection operator is defined and is used to create the images of electromagnetic fields and sources. The image fields satisfy Maxwell's equations, meaning that Maxwell's equations are invariant under the described reflection operations. By applying the reflection operations to media with reflection symmetry, the symmetry properties of the Stokes parameters, characterizing the polarization state of thermal emissions, are shown to agree with existing experimental data. The first two Stokes parameters are symmetric with respect to the reflection plane, while the third and fourth Stokes parameters have odd symmetry. In active remote sensing, the symmetry properties of the polarimetric scattering matrix elements of deterministic targets and the polarimetric covariance matrix elements of random media or distributed targets are examined. For deterministic targets, the cross-polarized responses are odd functions with respect to the symmetry direction, whereas the copolarized responses are even functions. For distributed targets or random media, it is found that the correlations of copolarized and cross-polarized responses are antisymmetric with respect to the reflection plane, while the other covariance matrix elements are symmetric. Consequently, in the cases of backscatter, the copolarized and cross-polarized components are completely uncorrelated when the incidence direction is on the symmetry plane. The derived symmetry properties of polarimetric backscattering coefficients agree with the predictions of a two-scale surface scattering model and existing sea surface HH and VV backscatter data. Finally, the conditions for a general type of media, i.e., bianisotropic media, to be reflection symmetric are examined.