Double diffusion transforms uniform background gradients of temperature and salinity into "staircases" of homogeneous mixed layers that are separated by high-gradient interfaces. Direct numerical simulations (DNS) and microstructure measurements are two independent methods of estimating double-diffusive fluxes. By performing DNS under similar conditions as found in our measurements in Lake Kivu, we are able to compare results from both methods for the first time. We find that (i) the DNS reproduces the measured interface thicknesses of in situ microstructure profiles, (ii) molecular heat fluxes through interfaces capture the total vertical heat fluxes for density ratios larger than three, and (iii) the commonly used heat flux parameterization underestimates the total fluxes by a factor of 1.3 to 2.2.