Based on the theory of distributions, this paper presents a simple derivation of the singularities and discontinuities associated with the eigenfunction expansions of the dyadic Green's functions for biisotropic media. The approach deals directly with Maxwell equations cast into dyadic forms prior to explicit determination of the dyadic Green's function formula. For both electric and magnetic dyadic Green's functions, the source point singularities are obtained without any integration and the discontinuities in their tangential and normal components across the source point are determined in compact forms directly from Maxwell dyadic equations. From the discontinuity relations, boundary conditions involving the tangential and normal components of electric and magnetic fields are derived. Due to the availability of different sets of constitutive relations characterizing a biisotropic medium, the singularities and discontinuities are discussed based on the commonly used Post-Jaggard and Drude-Born-Federov relations.