A surface integral equation (SIE) method is developed to analyze electromagnetic scattering by 3-D objects with soft-and-hard/DB (SHDB) boundary conditions. The SHDB boundary condition is a generalization of the soft-and-hard (SH) and DB boundary conditions that associate the normal and tangential field components on the boundary. In the developed method, the SHDB boundary condition is expressed in vector form that allows combining it with the tangential field integral equations. The obtained equations can be discretized with the standard method of moments (MoM) using the Rao-Wilton-Glisson (RWG) functions. Different combinations of the integral equations and boundary conditions are derived, and their numerical performance is studied and compared. It is demonstrated with numerical experiments that a much more stable system is obtained by considering the boundary conditions as extra equations, rather than integrating them into the SIEs. The solutions of the proposed nonsquare integral equation are verified with the physical optics approximations.