We present spectroscopy of stars in the immediate vicinity of the dwarf nova (DN) KZ Gem to confirm its identification, which is ambiguous in the literature. Analysis of 73 radial velocities spanning from 2014 to 2019 provides a high-precision orbital period of 0.2224628(2) days (similar to 5.34 hr) and shows KZ Gem to be a double-lined DN. Time series photometry taken from 2016 to 2018 shows a variable double-hump modulation with a full amplitude of similar to 0.3 mag, along with five Gaussian-like transient events lasting similar to 30 minutes or more. Using the light-curve code XRBinary and nonlinear fitting code NMfit, we obtain an optimized binary model of the dwarf nova (DN) KZ Gem, from time series photometry, consisting of a Roche-lobe-filling K-type dwarf with a mass transfer rate of (2.7-7.9) x 10(-10) M yr(-1) to a large, cool, and thick disk surrounding a white dwarf, in an orbit with an inclination of 516(14). Two hotspots on the disk are demonstrated to cause the observed variations in the ellipsoidal modulations from the secondary star. This physical model is compatible with the Gaia distance of KZ Gem.