We constrain the mass distribution in nearby, star-forming galaxies with the Star Formation Reference Survey (SFRS), a galaxy sample constructed to be representative of all known combinations of star formation rate (SFR), dust temperature, and specific star formation rate (sSFR) that exist in the Local Universe. An innovative two-dimensional bulge/disk decomposition of the 2MASS/$K_{s}$-band images of the SFRS galaxies yields global luminosity and stellar mass functions, along with separate mass functions for their bulges and disks. These accurate mass functions cover the full range from dwarf galaxies to large spirals, and are representative of star-forming galaxies selected based on their infra-red luminosity, unbiased by AGN content and environment. We measure an integrated luminosity density $j$ = 1.72 $pm$ 0.93 $times$ 10$^{9}$ L$_{odot}$ $h^{-1}$ Mpc$^{-3}$ and a total stellar mass density $rho_{M}$ = 4.61 $pm$ 2.40 $times$ 10$^{8}$ M$_{odot}$ $h^{-1}$ Mpc$^{-3}$. While the stellar mass of the emph{average} star-forming galaxy is equally distributed between its sub-components, disks globally dominate the mass density budget by a ratio 4:1 with respect to bulges. In particular, our functions suggest that recent star formation happened primarily in massive systems, where they have yielded a disk stellar mass density larger than that of bulges by more than 1 dex. Our results constitute a reference benchmark for models addressing the assembly of stellar mass on the bulges and disks of local ($z = 0$) star-forming galaxies.