  The mixed spin-1/2 and spin-3/2 Ising model on the extended Kagom\'e lattice
is solved by establishing a mapping correspondence with the eight-vertex model.
Letting the parameter of uniaxial single-ion anisotropy tend to infinity, the
model becomes exactly soluble as a free-fermion eight-vertex model. Under this
restriction, the critical points are characterized by critical exponents from
the standard Ising universality class. In a certain subspace of interaction
parameters that corresponds to a coexistence surface between two ordered
phases, the model becomes exactly soluble as a symmetric zero-field
eight-vertex model. This surface is bounded by a line of bicritical points that
have non-universal interaction-dependent critical exponents.
