Carrier-envelope phase difference effects in the dissociation of the HD+ molecular ion in the field of an intense, linearly polarized, ultrashort laser pulse are studied in the framework of the time-dependent Schrödinger equation. We consider a reduced-dimensionality model in which the nuclei are free to vibrate along the field polarization and the electrons move in two dimensions. The laser has a central wavelength of 790 nm and a pulse length of 10 fs with intensities in the range 6x10(14) to 9x10(14) W/cm(2). We find that the angular distribution of dissociation to p+D and H+d can be controlled by varying the phase difference, generating differences between the dissociation channels of more than a factor of 2. Moreover, the asymmetry is nearly as large for H+2 dissociation.