Two kinds of multidimensional atom interferometers are demonstrated that are capable of measuring both the magnitude and direction of applied inertial forces. These interferometers, built from ultracold Bose-Einstein condensed rubidium atoms, use an original design that operates entirely within the Bloch bands of an optical lattice. Through time-dependent lattice position control, we realize Bloch oscillations in two dimensions and a vector atomic Michelson interferometer. Fits to the observed Bloch oscillations demonstrate the measurement of an applied acceleration of 2 g along two axes, where g is Earth’s gravitational acceleration. For the Michelson interferometer, we perform Bayesian inferencing from a 49-channel output by repeating experiments for two-axis accelerations and demonstrate vector parameter estimation. Accelerations can be measured from single experimental runs and do not require repeated shots to construct a fringe. The performance of our device is near the quantum limit for the interferometer size and quantum detection efficiency of the atoms.