  We present the discovery of strong Balmer line absorption in H$\alpha$ to
H$\gamma$ in two luminous low-ionization broad absorption line quasars (LoBAL
QSOs) at z~1.5, with black hole masses around $10^{10}$ $M_\odot$ from near-IR
spectroscopy. There are only two previously known quasars at z>1 showing Balmer
line absorption. SDSS J1019+0225 shows blueshifted absorption by ~1400 km/s
with an H$\alpha$ rest-frame equivalent width of 13 \AA{}. In SDSS J0859+4239
we find redshifted absorption by ~500 km/s with an H$\alpha$ rest-frame
equivalent width of 7 \AA{}. The redshifted absorption could indicate an inflow
of high density gas onto the black hole, though we cannot rule out alternative
interpretations. The Balmer line absorption in both objects appears to be
saturated, indicating partial coverage of the background source by the
absorber. We estimate the covering fractions and optical depth of the absorber
and derive neutral hydrogen column densities, $N_{\rm{H\,I}}\sim1.3\times
10^{18}$ cm$^{-2}$ for SDSS J1019+0225 and $N_{\rm{H\,I}}\sim9\times 10^{17}$
cm$^{-2}$ for SDSS J0859+4239, respectively. In addition, the optical spectra
reveal also absorption troughs in HeI* $\lambda3889$ and $\lambda3189$ in both
objects.
