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 \sim 1.5 , with black hole masses around 10 ^ { 10 } M _ { \odot } from near-IR spectroscopy . There are only two previously known quasars at z > 1.0 showing Balmer line absorption . SDSS J1019+0225 shows blueshifted absorption by \sim 1400 km s ^ { -1 } with an H \alpha rest-frame equivalent width of 13 Å . In SDSS J0859+4239 we find redshifted absorption by \sim 500 km s ^ { -1 } with an H \alpha rest-frame equivalent width of 7 Å . The redshifted absorption could indicate an inflow of high density gas onto the black hole , though we can not 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 _ { H I } \sim 1.3 \times 10 ^ { 18 } cm ^ { -2 } for SDSS J1019+0225 and N _ { H I } \sim 9 \times 10 ^ { 17 } cm ^ { -2 } for SDSS J0859+4239 . In addition , the optical spectra reveal also absorption troughs in He i ^ { * } \lambda 3889 and \lambda 3189 in both objects .