The dissociation of an H_{2}^{+} molecular-ion beam by linearly polarized, carrier-envelope-phase-tagged 5 fs pulses at 4×10^{14} W/cm^{2} with a central wavelength of 730 nm was studied using a coincidence 3D momentum imaging technique. Carrier-envelope-phase-dependent asymmetries in the emission direction of H^{+} fragments relative to the laser polarization were observed. These asymmetries are caused by interference of odd and even photon number pathways, where net zero-photon and one-photon interference predominantly contributes at H^{+}+H kinetic energy releases of 0.2-0.45 eV, and net two-photon and one-photon interference contributes at 1.65-1.9 eV. These measurements of the benchmark H_{2}^{+} molecule offer the distinct advantage that they can be quantitatively compared with ab initio theory to confirm our understanding of strong-field coherent control via the carrier-envelope phase.