  We find a combinatorial interpretation of Shareshian and Wachs'
$q$-binomial-Eulerian polynomials, which leads to an alternative proof of their
$q$-$\gamma$-positivity using group actions. Motivated by the sign-balance
identity of D\'esarm\'enien--Foata--Loday for the $(\mathrm{des},
\mathrm{inv})$-Eulerian polynomials, we further investigate the sign-balance of
the $q$-binomial-Eulerian polynomials. We show the unimodality of the resulting
signed binomial-Eulerian polynomials by exploiting their continued fraction
expansion and making use of a new quadratic recursion for the
$q$-binomial-Eulerian polynomials. We finally use the method of continued
fractions to derive a new $(p,q)$-extension of the $\gamma$-positivity of
binomial-Eulerian polynomials which involves crossings and nestings of
permutations.
