A self-consistent model of the tangential magnetopause is formulated on the basis of the Vlasov-Maxwell equations. In this model the plasmas on both sides are magnetized; the magnetic field is assumed everywhere parallel to the magnetopause (i.e., the normal component Bn=0) and is allowed to rotate through an arbitrary angle across the magnetopause. It is shown that the thickness of the magnetopause is greater than the gyroradius of the hotter species of the plasmas (the ions). The presence of a trapped particle population inside the magnetopause is shown to be required in order to allow the magnetic field to rotate more than a certain critical angle (~90¿). The observed 'bulge-out' feature in B vector hodograms is found to be due to lack of overlap between plasmas from the two sides of the magnetopause. An electric field normal to the magnetopause is present in our model, with magnitudes from 0.1 to 10 mV/m, depending primarily on the relative flow speed parallel to the magnetopause between plasmas on the two sides. The magnetopause current in our model is carried predominantly by the ions and has a significant field-aligned component. The magnetopause current is a possible source of field-aligned currents on cusp as well as auroral oval field lines. The proposed model can reproduce the observed features of the tangential magnetopause structure by specifying boundary conditions on both sides of the magnetopause. It also provides a basis for understanding the electric and magnetic fields, the current and the stability of the tangential magnetopause in terms of the collective particle dynamics.