  We construct a set of lattice models of non-interacting topological
insulators with chiral symmetry in three dimensions. We build a model of the
topological insulators in the class AIII by coupling lower dimensional models
of $\mathbb{Z}$ classes. By coupling the two AIII models related by
time-reversal symmetry we construct other chiral symmetric topological
insulators that may also possess additional symmetries (the time-reversal
and/or particle-hole).
  There are two different chiral symmetry operators for the coupled model, that
correspond to two distinct ways of defining the sublattices. The integer
topological invariant (the winding number) in case of weak coupling can be
either the sum or difference of indices of the basic building blocks, dependent
on the preserved chiral symmetry operator. The value of the topological index
in case of weak coupling is determined by the chiral symmetry only and does not
depend on the presence of other symmetries. For $\mathbb{Z}$ topological
classes AIII, DIII, and CI with chiral symmetry are topologically equivalent,
it implies that a smooth transition between the classes can be achieved if it
connects the topological sectors with the same winding number. We demonstrate
this explicitly by proving that the gapless surface states remain robust in
$\mathbb{Z}$ classes as long as the chiral symmetry is preserved, and the
coupling does not close the gap in the bulk. By studying the surface states in
$\mathbb{Z}_2$ topological classes, we show that class CII and AII are
distinct, and can not be adiabatically connected.
