  The Landau bands of mirror symmetric 2D Dirac semi-metals (for example
odd-layers of ABA-graphene) can be identified by their parity with respect to
mirror symmetry. This symmetry facilitates a new class of counter-propagating
Hall states at opposite but equal electron and hole filling factors
$|\nu_{\pm}|=1/m$ ({\it m} odd). Here, we propose a Laughlin-like correlated
liquid wavefunction, at the charge neutrality point, that exhibits fractionally
charged quasi-particle/hole pair excitation of opposite parity. Using a
bosonized one-dimensional edge state theory, we show that the longitudinal
conductance of this state, $\sigma_{xx} = 2e^2/(m h)$, is robust to
short-ranged inter-mode interactions.
