In this paper a spring-like micromechanical contact model is proposed, aiming to describe the mechanical behavior of two rough surfaces in no-sliding contact under a closure pressure. The contact region between two elastic bodies is described as a thin damaged interphase characterized by the occurrence of non-interacting penny-shaped cracks (internal cracks). By combining a homogenization approach and an asymptotic technique, tangential and normal equivalent contact stiffnesses are consistently derived. An analytical description of evolving contact and no-contact areas with respect to the closure pressure is also provided, resulting consistent with theoretical Hertz-based asymptotic predictions and in good agreement with available numerical estimates. Proposed model has been successfully validated through comparisons with some theoretical and experimental results available in literature, as well as with other well-established modeling approaches. Finally, the influence of main model parameters is addressed, proving also the model capability to catch the experimentally-observed dependence of the tangent-to-normal contact stiffness ratio on the closure pressure.