The MBE-grown GaAs/AlGaAs superlattice with Si-doped barriers has been used to study a 3D→2D transition under the influence of the in-plane component of an applied magnetic field. The longitudinal magnetoresistance data measured in tilted magnetic fields have been interpreted in terms of a simple tight-binding model. The data provide values of basic parameters of the model and make it possible to reconstruct the superlattice Fermi surface and to calculate the density of states for the lowest Landau subbands. Positions of van Hove singularities in the DOS agree excellently with magnetoresistance oscillations, confirming that the model describes adequately the magnetoresistance of strongly coupled semiconductor superlattices.