An improved analytical solution to the two-layer transmission line model for determining contact resistances to semiconductor layers is presented. In contrast to previously published two-layered analyses, the present solution is valid for arbitrary strength linear coupling between the two conducting layers in the region under the contact. A comparison of limiting cases and a physical interpretation of the differences between predictions of this model and previous models are presented. The predicted resistance versus pad separation behaviour obtained from the present model and from a two-layer model which assumed weak interlayer coupling beneath the contacts are compared for identical physical structures. Experimental data for contact resistance measurements on a double-barrier resonant tunneling diode structure are presented. The measured data exhibit the nonlinear resistance versus pad spacing predicted by the model and show a dependence on current level which can be modelled as a variation of the interlayer coupling strength. The values of the contact resistance, interlayer coupling resistance and sheet resistance extracted from the measured data using the present model and the weakly coupled model are presented and compared with independently measured and calculated parameters.