We study near-infrared (JHK) and X-ray light curves of Cyg X-3 obtained with the 2.5m telescope of the Caucasian Mountain Observatory of MSU SAI and collected from the RXTE ASM and MAXI archives. The light curves in the X-ray and IR domains are strongly affected by irregular variations. However, the mean curves are remarkably stable and qualitatively similar in both domains. This means that the IR flux of the system originates not only from the free-free radiation of the Wolf-Rayet (WR) wind but also from a compact IR source located near the relativistic companion. The shape of the mean X-ray and IR light curves suggest the existence of two additional structures in the WR wind-a bow shock near the relativistic companion and a so-called "clumpy trail." Modeling of the mean X-ray and IR light curves allowed us to obtain important system parameters: the orbital phase of the superior conjunction of the relativistic companion ph_0_=-0.066+/-0.006, the orbital inclination angle i=29.5{deg}+/-1.2{deg}, and the WR mass-loss rate dM/dt=(0.96+/-0.14)x10^-5^M_{sun}/yr. By using relations between dM/dt and the rate of the period change and between dM/dt and the WR mass, we estimated the probable mass of the relativistic companion M_C~7.2M_{sun}_, which points toward the black hole hypothesis. However, this estimate is based on the assumption of a smooth WR wind. Considering the uncertainty associated with clumping, the mass-loss rate can be lower, which leaves room for the neutron star hypothesis.