We analyze the photonic topological phases in bianisotropic metamaterials characterized by a lossless and reciprocal magnetoelectric tensor. The underlying medium is considered a topological insulator that supports a pair of counterpropagating helical edge states. By introducing the pseudospin basis, the photonic system can be described by the spin-orbit Hamiltonians with spin 1, which result in nonzero spin Chern numbers that determine the topological properties. Surface modes at the interface between two bianisotropic media with opposite chirality exist in their common band gap, which are represented by elliptic or hyperbolic equations. In particular, two branches of hyperbolic surfaces are degenerate at the frequency where the chiral nihility occurs, which depict the helical nature of edge states between two distinct topological phases. Topological features of the bianisotropic metamaterials are further illustrated with the robust transport of surface modes at an irregular boundary.