  We study the many-body ground states of two-component hardcore bosons in
topological triangular lattice models. Utilizing exact diagonalization and
density-matrix renormalization group calculations, we demonstrate that at
commensurate two-thirds filling per lattice site, two-component bosonic integer
quantum hall (BIQH) effect emerges with the associated
$\mathbf{K}=\begin{pmatrix} 0 & 1\\ 1 & 0\\ \end{pmatrix}$ matrix under strong
intercomponent Hubbard repulsion. The topological nature is further elucidated
by (i) a unique ground state degeneracy with a robust spectrum gap, (ii) a
quantized topological Chern number matrix $\mathbf{C}=\mathbf{K}^{-1}$, and
(iii) two counterpropagating edge branches. Moreover, with increasing
nearest-neighbor repulsions, the ground state undergoes a first-order
transition from a BIQH liquid to a commensurate solid order.
