We study large-scale outflows in a sample of 96 star-forming galaxies at 1<z<2, using near-UV spectroscopy of FeII and MgII absorption and emission. The average blueshift of the FeII interstellar absorption lines with respect to the systemic velocity is -85+/-10 km/s at z~1.5, with standard deviation 87 km/s; this is a decrease of a factor of two from the average blueshift measured for far-UV interstellar absorption lines in similarly selected galaxies at z~2. The profiles of the MgII 2796, 2803 lines show much more variety than the FeII profiles, which are always seen in absorption; MgII ranges from strong emission to pure absorption, with emission more common in galaxies with blue UV slopes and at lower stellar masses. Outflow velocities, as traced by the centroids and maximum extent of the absorption lines, increase with increasing stellar mass with 2-3sigma significance, in agreement with previous results. We study fine structure emission from FeII*, finding several lines of evidence in support of the model in which this emission is generated by the re-emission of continuum photons absorbed in the FeII resonance transitions in outflowing gas. In contrast, photoionization models indicate that MgII emission arises from the resonant scattering of photons produced in HII regions, accounting for the differing profiles of the MgII and FeII lines. A comparison of the strengths of the FeII absorption and FeII* emission lines indicates that massive galaxies have more extended outflows and/or greater extinction, while two-dimensional composite spectra indicate that emission from the outflow is stronger at a radius of ~10 kpc in high mass galaxies than in low mass galaxies.