  We analyze experimentally and theoretically the transport spectra of a gated
lateral GaAs double quantum dot containing two holes. The strong spin-orbit
interaction present in the hole subband lifts the Pauli spin blockade and
allows to map out the complete spectra of the two-hole system. By performing
measurements in both source-drain voltage directions, at different detunings
and magnetic fields, we carry out quantitative fitting to a Hubbard two-site
model accounting for the tunnel coupling to the leads and the spin-flip
relaxation process. We extract the singlet-triplet gap and the magnetic field
corresponding to the singlet-triplet transition in the double-hole ground
state. Additionally, at the singlet-triplet transition we find a resonant
enhancement (in the blockaded direction) and suppression of current (in the
conduction direction). The current enhancement stems from the multiple
resonance of two-hole levels, opening several conduction channels at once. The
current suppression arises from the quantum interference of spin-conserving and
spin flipping tunneling processes.
