Despite the demonstrated benefits of bimanual interaction, most tablets use just one hand for interaction, to free the other for support. In a preliminary study, we identified five holds that permit simultaneous support and interaction, and noted that users frequently change position to combat fatigue. We then designed the BiTouch design space, which introduces a support function in the kinematic chain model for interacting with hand-held tablets, and developed BiPad, a toolkit for creating bimanual tablet interaction with the thumb or the fingers of the supporting hand. We ran a controlled experiment to explore how tablet orientation and hand position affect three novel techniques: bimanual taps, gestures and chords. Bimanual taps outperformed our one-handed control condition in both landscape and portrait orientations; bimanual chords and gestures in portrait mode only; and thumbs outperformed fingers, but were more tiring and less stable. Together, BiTouch and BiPad offer new opportunities for designing bimanual interaction on hand-held tablets.