  The graded parafermion conformal field theory at level k is a close cousin of
the much-studied Z_k parafermion model. Three character formulas for the graded
parafermion theory are presented, one bosonic, one fermionic (both previously
known) and one of spinon type (which is new). The main result of this paper is
a proof of the equivalence of these three forms using q-series methods combined
with the combinatorics of lattice paths. The pivotal step in our approach is
the observation that the graded parafermion theory -- which is equivalent to
the coset osp(1,2)_k/ u(1) -- can be factored as (osp(1,2)_k/ su(2)_k) x
(su(2)_k/ u(1)), with the two cosets on the right equivalent to the minimal
model M(k+2,2k+3) and the Z_k parafermion model, respectively. This
factorisation allows for a new combinatorial description of the graded
parafermion characters in terms of the one-dimensional configuration sums of
the (k+1)-state Andrews--Baxter--Forrester model.
