  The effect of the built-in supersymmetric quantum mechanical language on the
spectrum of the (1+1)-Dirac equation, with position-dependent mass (PDM) and
complexified Lorentz scalar interactions, is re-emphasized. The signature of
the "quasi-parity" on the Dirac particles' spectra is also studied. A Dirac
particle with PDM and complexified scalar interactions of the form S(z)=S(x-ib)
(an inversely linear plus linear, leading to a PT-symmetric oscillator model),
and S(x)=S_{r}(x)+iS_{i}(x) (a PT-symmetric Scarf II model) are considered.
Moreover, a first-order intertwining differential operator and an
$\eta$-weak-pseudo-Hermiticity generator are presented and a complexified
PT-symmetric periodic-type model is used as an illustrative example.
