  In this work, we explore the existence of traversable wormhole solutions
supported by double gravitational layer thin-shells and satisfying the Null
Energy Condition (NEC) throughout the whole spacetime, in a quadratic-linear
form of the generalized hybrid metric-Palatini gravity. We start by showing
that for a particular quadratic-linear form of the action, the junction
conditions on the continuity of the Ricci scalar $R$ and the Palatini Ricci
scalar $\mathcal R$ of the theory can be discarded without the appearance of
undefined distribution terms in the field equations. As a consequence, a double
gravitational layer thin-shell arises at the separation hypersurface. We then
outline a general method to find traversable wormhole solutions satisfying the
NEC at the throat and provide an example. Finally, we use the previously
derived junction conditions to match the interior wormhole solution to an
exterior vacuum and asymptotic flat solution, thus obtaining a full traversable
wormhole solution supported by a double gravitational layer thin-shell and
satisfying the NEC. Unlike the wormhole solutions previously obtained in the
scalar-tensor representation of this theory, which were scarce and required
fine-tuning, the solutions obtained through this method are numerous and exist
for a wide variety of metrics and actions.
