  We analyse the parallel hybrid texture structures in the charged lepton and
the neutrino sector. These parallel hybrid texture structures have physical
implications as they cannot be obtained from arbitrary lepton mass matrices
through weak basis transformations. The total sixty parallel hybrid texture
structures can be grouped into twelve classes, and all the hybrid textures in
the same class have identical physical implications. We examine all the twelve
classes under the assumption of non-factorizable phases in the neutrino mass
matrix. Five out of the total twelve classes are found to be phenomenologically
disallowed. We study the phenomenological implications of the allowed classes
for 1-3 mixing angle, Majorana and Dirac-type $CP$ violating phases.
Interesting constraints on effective Majorana mass are obtained for all the
allowed classes.
