We present grism spectra of emission-line galaxies (ELGs) from 0.6-1.6 microns from the Wide Field Camera 3 on the Hubble Space Telescope. These new infrared grism data augment previous optical Advanced Camera for Surveys G800L 0.6-0.95 micron grism data in GOODS-South from the PEARS program, extending the wavelength covereage well past the G800L red cutoff. The ERS grism field was observed at a depth of 2 orbits per grism, yielding spectra of hundreds of faint objects, a subset of which are presented here. ELGs are studied via the Ha, [OIII], and [OII] emission lines detected in the redshift ranges 0.2<z<1.4, 1.2<z<2.2 and 2.0<z<3.3 respectively in the G102 (0.8-1.1 microns; R~210) and G141 (1.1-1.6 microns; R~130) grisms. The higher spectral resolution afforded by the WFC3 grisms also reveals emission lines not detectable with the G800L grism (e.g., [SII] and [SIII] lines). From these relatively shallow observations, line luminosities, star-formation rates, and grism spectroscopic redshifts are determined for a total of 48 ELGs to m(AB)~25 mag. Seventeen GOODS-South galaxies that previously only had photometric redshifts now have new grism-spectroscopic redshifts, in some cases with large corrections to the photometric redshifts (Delta(z)~0.3-0.5). Additionally, one galaxy had no previously-measured redshift but now has a secure grism-spectroscopic redshift, for a total of 18 new GOODS-South spectroscopic redshifts. The faintest source in our sample has a magnitude m(AB)=26.9 mag. The ERS grism data also reflect the expected trend of lower specific star formation rates for the highest mass galaxies in the sample as a function of redshift, consistent with downsizing and discovered previously from large surveys. These results demonstrate the remarkable efficiency and capability of the WFC3 NIR grisms for measuring galaxy properties to faint magnitudes and redshifts to z>2.