  We study modulational instability of two-component Bose-Einstein condensates
in an optical lattice, which is modelled as a coupled discrete nonlinear Schr
\"{o}dinger equation. The excitation spectrum and the modulational instability
condition of the total system are presented analytically. In the
long-wavelength limit, our results agree with the homogeneous two-component
Bose-Einstein condensates case. The discreteness effects result in the
appearance of the modulational instability for the condensates in miscible
region. The numerical calculations confirm our analytical results and show that
the interspecies coupling can transfer the instability from one component to
another.
