IRAS F11119+3257 is a quasar-dominated ultraluminous infrared galaxy, with a partially obscured narrow-line Seyfert 1 nucleus. In this paper, we present the near-IR (NIR) spectroscopy of F11119+3257, in which we find unusual Paschen emission lines and metastable He I* lambda 10830 absorption associated with the previously reported atomic sodium and molecular OH mini-BAL (broad absorption line) outflow. Photoionization diagnosis confirms previous findings that the outflows are at kiloparsec scales. Such large-scale outflows should produce emission lines. We indeed find that high-ionization emission lines ([O III], [Ne III], and [Ne V]) are dominated by blueshifted components at similar speeds to the mini-BALs. The blueshifted components are also detected in some low-ionization emission lines, such as [O II] lambda 3727 and some Balmer lines (H alpha, H beta, and H gamma), even though their cores are dominated by narrow (FWHMNEL = 570 +/- 40 km s(-1)) or broad components at the systemic redshift of z = 0.18966 +/- 0.00006. The mass flow rate (230-730 M-circle dot yr(-1)) and the kinetic luminosity ((E)over dot(k) similar to 10(43.6-44.8) erg s(-1)) are then inferred jointly from the blueshifted emission and absorption lines. In the NIR spectrum of F11119+3257, we also find that the Paschen emission lines are unique, in which a very narrow (FWHM = 260 +/- 20 km s(-1)) component is shown in only Pa alpha. This narrow component most probably comes from heavily obscured star formation. Based on the Pa alpha and Pa beta emissions, we obtain an extinction at the H band, A(H) > 2.1 (or a reddenning of EB-V > 3.7), and a star formation rate of SFR > 130 M-circle dot yr(-1) that resembles the estimates inferred from the far-IR emissions (SFRFIR = 190 +/- 90 M-circle dot yr(-1)).