We present GaussBits, which is a system of the passive magnetic tangible designs that enables 3D tangible interactions in the near-surface space of portable displays. When a thin magnetic sensor grid is attached to the back of the display, the 3D position and partial 3D orientation of the GaussBits can be resolved by the proposed bi-polar magnetic field tracking technique. This portable platform can therefore enrich tangible interactions by extending the design space to the near-surface space. Since non-ferrous materials, such as the user's hand, do not occlude the magnetic field, interaction designers can freely incorporate a magnetic unit into an appropriately shaped non-ferrous object to exploit the metaphors of the real-world tasks, and users can freely manipulate the GaussBits by hands or using other non-ferrous tools without causing interference. The presented example applications and the collected feedback from an explorative workshop revealed that this new approach is widely applicable.