Developing new allotropes with excellent properties and high synthesizability is an intriguing and challenging topic for carbon materials. Based on the experimental biphenylene monolayers, varied three-dimensional crystalline foam carbon allotropes with parallel channels in the structure are theoretically designed. These calculated foam carbon structures are mostly semimetals or semiconductors. The selected representatives possess lattice dynamic stability, high thermal stability, great mechanical performance stability, and feasible synthesizability. Moreover, the selected foam carbon structures exhibit high feasibility in ion filtration, transport, or storage for different ion species. The representative structure (3D-C