Summary: The three-dimensional mean spherical model with an \(L\)-layer film geometry is considered under Neumann-Neumann and Neumann-Dirichlet boundary conditions. Surface fields \(h_1\) and \(h_L\) are supposed to act at the surfaces bounding the system. In the case of Neumann boundary conditions, a new surface critical exponent \(\Delta^{\text{sb}}_1={3\over 2}\) is found. It is argued that this exponent corresponds to a special (surface-bulk) phase transition in the model. The Privman-Fisher scaling hypothesis for the free energy is verified and the corresponding scaling functions for both the Neumann-Neumann and Neumann-Dirichlet boundary conditions are explicitly derived. If the layer field is applied at some distance from the Dirichlet boundary, a family of critical exponents emerges: their values depend on the exponent defining how the distance scales with the finite size of the system, and they interpolate continuously between the extreme cases \(\Delta^{\text{o}}_1={1\over 2}\) and \(\Delta^{\text{sb}}_1={3\over 2}\).