An intense phase-controlled orthogonally polarized two-color ultrashort laser pulse is used to singly ionize and dissociate H_{2} into a neutral hydrogen atom and a proton. Emission-direction and kinetic-energy dependent asymmetric dissociation of H_{2} is observed as a function of the relative phase of the orthogonally polarized two-color pulse. Significant asymmetric proton emission is measured in the direction between two polarization axes. Our numerical simulations of the time-dependent Schrödinger equation reproduce many of the observed features. The asymmetry is attributed to the coherent superposition of two-dimensional nuclear wave packets with opposite parities, which have the same energies and overlap in the same emission directions.