  We present a general theoretical formulation to describe the interlayer
interaction in incommensurate bilayer systems with arbitrary crystal
structures. By starting from the tight- binding model with the
distance-dependent transfer integral, we show that the interlayer coupling,
which is highly complex in the real space, can be simply written in terms of
generalized Umklapp process in the reciprocal space. The formulation is useful
to describe the interaction in the two-dimensional interface of different
materials with arbitrary lattice structures and relative orientations. We apply
the method to the incommensurate bilayer graphene with a large rotation angle,
which cannot be treated as a long-range moir\'{e} superlattice, and obtain the
quasi band structure and density of states within the first-order
approximation.
