We analyze the gravitational binary-lensing event OGLE-2016-BLG-0156 , for which the lensing light curve displays pronounced deviations induced by microlens-parallax effects . The light curve exhibits 3 distinctive widely-separated peaks and we find that the multiple-peak feature provides a very tight constraint on the microlens-parallax effect , enabling us to precisely measure the microlens parallax \pi _ { E } . All the peaks are densely and continuously covered from high-cadence survey observations using globally located telescopes and the analysis of the peaks leads to the precise measurement of the angular Einstein radius \theta _ { E } . From the combination of the measured \pi _ { E } and \theta _ { E } , we determine the physical parameters of the lens . It is found that the lens is a binary composed of two M dwarfs with masses M _ { 1 } = 0.18 \pm 0.01 M _ { \odot } and M _ { 2 } = 0.16 \pm 0.01 M _ { \odot } located at a distance D _ { L } = 1.35 \pm 0.09 { kpc } . According to the estimated lens mass and distance , the flux from the lens comprises an important fraction , \sim 25 \% , of the blended flux . The bright nature of the lens combined with the high relative lens-source motion , \mu = 6.94 \pm 0.50 { mas } { yr } ^ { -1 } , suggests that the lens can be directly observed from future high-resolution follow-up observations .