  A reflection-asymmetric triaxial particle rotor model (RAT-PRM) with a
quasi-proton and a quasi-neutron coupled with a reflection-asymmetric triaxial
rotor is developed and applied to investigate the multiple chiral doublet
(M$\chi$D) bands candidates with octupole correlations in $^{78}$Br. The
calculated excited energies, energy staggering parameters, and $B(M1)/B(E2)$
ratios are in a reasonable agreement with the data of the chiral doublet bands
with positive- and negative-parity. The influence of the triaxial deformation
$\gamma$ on the calculated $B(E1)$ is found to be significant. By changing
$\gamma$ from 16$^\circ$ to 21$^\circ$, the $B(E1)$ values will be enhanced and
better agreement with the $B(E1)/B(E2)$ data is achieved. The chiral geometry
based on the angular momenta for the rotor, the valence proton and valence
neutron is discussed in details.
