The mutually complementary Euclid and Roman galaxy redshift surveys will use Hα-and [O iii]-selected emission-line galaxies (ELGs) as tracers of the large-scale structure at 0.9 ≲ z ≲ 1.9 (Hα) and 1.5 ≲ z ≲ 2.7 ([O iii]). It is essential to have a reliable and sufficiently precise knowledge of the expected numbers of Hα-emitting galaxies in the survey volume in order to optimize these redshift surveys for the study of dark energy. Additionally, these future samples of ELGs will, like all slitless spectroscopy surveys, be affected by a complex selection function that depends on galaxy size and luminosity, line equivalent width (EW), and redshift errors arising from the misidentification of single ELGs. Focusing on the specifics of the Euclid survey, we combine two slitless spectroscopic WFC3-IR data sets-3D-HST+AGHAST and the WFC3 Infrared Spectroscopic Parallel survey-to construct a Euclid-like sample that covers an area of 0.56 deg2 and includes 1277 ELGs. We detect 1091 (∼3270 deg-2) Hα+[N ii]-emitting galaxies in the range 0.9 ≤ z ≤ 1.6 and 162 (∼440 deg-2) [O iii] λ5007 emitters over 1.5 ≤ z ≤ 2.3 with line fluxes ≥2 × 10-16 erg s-1 cm-2. The median of the Hα+[N ii] EW distribution is ∼250 Å, and the effective radii of the continuum and Hα+[N ii] emission are correlated with a median of ∼0.″38 and significant scatter (σ ∼ 0.″2-0.″35). Finally, we explore the prevalence of redshift misidentification in future Euclid samples, finding potential contamination rates of ∼14%-20% and ∼6% down to 2 × 10-16 erg s-1 cm-2 and 6 × 10-17 erg s-1 cm-2, respectively, although with increased wavelength coverage these percentages drop to nearly zero.