We present the optical and near-infrared luminosity and mass functions of the local star-forming galaxies in the Universidad Complutense de Madrid (UCM) Survey. A bivariate method that explicitly deals with the Hα selection of the survey is used when estimating these functions. Total stellar masses have been calculated on a galaxy-by-galaxy basis taking into account differences in star formation histories. The main difference between the luminosity distributions of the UCM sample and the luminosity functions of the local galaxy population is a lower normalization (*), indicating a lower global volume density of UCM galaxies. The typical near-infrared luminosity (L*) of local star-forming galaxies is fainter than that of normal galaxies. This is a direct consequence of the lower stellar masses of our objects. However, at optical wavelengths (B and r), the luminosity enhancement arising from the young stars leads to M* values that are similar to those of normal galaxies. The fraction of the total optical and near-infrared luminosity density in the local universe associated with star-forming galaxies is 10%-20%. Fitting the total stellar mass function using a Schechter parameterization, we obtain α = -1.15 ± 0.15, log * = 10.82 ± 0.17 ☉, and log * = -3.04 ± 0.20 Mpc-3. This gives an integrated total stellar mass density of 107.83±0.07 ☉ Mpc-3 in local star-forming galaxies (H0 = 70 km s-1 Mpc-1, ΩM = 0.3, and Λ = 0.7). The volume-averaged burst strength of the UCM galaxies is b = 0.04 ± 0.01, defined as the ratio of the mass density of stars formed in recent bursts (with an age of <10 Myr) to the total stellar mass density in UCM galaxies. Finally, we derive that in the local universe, 13% ± 3% of the total baryon mass density in the form of stars is associated with star-forming galaxies.