We demonstrate a method to fully characterize mass-transferring double white dwarf (DWD) systems with a helium-rich (He) WD donor based on the mass--radius relationship for He WDs. Using a simulated Galactic population of DWDs, we show that donor and accretor masses can be inferred for up to $sim, 60$ systems observed by both Laser Interferometer Space Antenna (LISA) and Gaia. Half of these systems will have mass constraints $Delta,M_{rm{D}}lesssim0.2M_{odot}$ and $Delta,M_{rm{A}}lesssim2.3,M_{odot}$. We also show how the orbital frequency evolution due to astrophysical processes and gravitational radiation can be decoupled from the total orbital frequency evolution for up to $sim 50$ of these systems.