A hinge assembly for an appliance includes features that allow for a door rotatably hinged to the appliance to be raised or lowered through various phases of the swing arc of the door by utilizing a ramped surface of a bracket of the hinge assembly as the working surface. In one exemplary aspect, a hinge assembly includes a hinge bracket having a pivot pin and a ramped surface. The door hinge assembly also includes a cam assembly coupled with the door and having a cam projection. As the door is swung about its swing arc, the cam projection engages the ramped surface of the hinge bracket. In this way, the door can be raised along the vertical direction as the door is rotated through its swing arc.