We present a spectral method of configuration-interaction type for three-dimensional helium which combines the complex rotation method with an appropriate expansion of the atom wave function in a basis of products of Coulomb-Sturmian functions of the electron radial coordinates with independent dilation parameters for the two electrons and bipolar spherical harmonics of the angular coordinates. The matrix elements of the kinetic energy and of the electron-nucleus interaction term are calculated using Gauss-Laguerre integration techniques. A combination of Gauss-Laguerre integration techniques with the generalized Wigner-Eckart theorem and recurrence relations allows an efficient and stable calculation of the matrix elements of the electron-electron interaction. The freedom of the choice of the dilation parameters permits us to access highly excited states with rather small sizes of the basis. Highly doubly excited states up to the tenth ionization threshold of singlet and triplet $S$ states of helium are presented.