The MAJORANA DEMONSTRATOR is a 76Ge-based neutrinoless double-beta decay (0νββ) experiment. Staged at the 4850 ft level of the Sanford Underground Research Facility, the DEMONSTRATOR operates an array of high-purity p-type point contact Ge detectors deployed within a graded passive shield and an active muon veto system. The present work concerns the two-neutrino double-beta decay mode (2νββ) of 76Ge. For Ge detectors, having superior energy resolution (0.1%), this mode poses negligible background to the 0νββ mode, even for a ton-scale experiment. However, the measurement of the 2νββ mode allows for careful systematics checks of active detector mass, enrichment fraction, and pulse shape discrimination cuts related to both the 0νββ and 2νββ decay modes. A precision measurement of the 2νββ shape also allows searches for spectral distortions, possibly indicative of new physics, including 0νββχ. Work is underway to construct a full experimental background model enabling a Bayesian fit to the measured energy spectrum and extraction of a precise 2νββ spectrum and half-life.