  We explore the collective excitations of optical lattices filled with
two-species Bose-Einstein condensates (TBECs). We use a set of coupled discrete
nonlinear Schr\"odinger equations to describe the system, and employ
Hartree-Fock-Bogoliubov (HFB) theory with the Popov approximation to analyze
the quasiparticle spectra at zero temperature. The ground state geometry,
evolution of quasiparticle energies, structure of quasiparticle amplitudes, and
dispersion relations are examined in detail. The trends observed are in stark
contrast to the case of TBECs only with a harmonic confining potential. One key
observation is the quasiparticle energies are softened as the system is tuned
towards phase separation, but harden after phase separation and mode
degeneracies are lifted.
