Tablets are often used as a distant input device to interact with large displays. Users can hold the tablet with two hands when interacting for a long time to avoid fatigue or dropping it. Still, most previous distant interaction techniques consider only one-handed tablets. This paper presents novel interaction techniques to perform distant pointing and command selection tasks using both thumbs while holding the device with two hands. In a first step, we design and evaluate six interaction techniques for distant pointing, based on using one or two thumbs, absolute or relative cursor control and single- or dual-precision pointing. Our results show that a combination of dual-thumb and relative pointing is preferred and more efficient than any other dual-thumb or single-thumb technique we designed. In a second step, we focus on command selection using two thumbs. We designed seven dual-thumb menu techniques based on quarter-pie or half-pie layouts, offering from 64 to 900 items. Our results show that using quarter-pie menu techniques is more efficient, usable and appreciated than using a linear or half-pie menu. Furthermore, we show that augmenting the number of items for quarter-pie and half-pie menu techniques has a low impact on command selection performance. In a third step, we compare our quarter-pie menus to bimanual marking menus. Our results show that quarter-pie menus are more efficient and less error-prone. We finally provide a set of lessons for designing efficient dual-thumb interaction techniques for two-handed tablets.