In this talk, we introduce a family of high-order enriched finite element methods for discontinuous solutions of interface elliptic and parabolic problems. It has the ability to handle implicit jump conditions as well as explicit ones. The optimal order convergence in broken Sobolev norms and superconvergence behavior at the nodes will be discussed. Several numerical examples will be shown. In particular, the method is applied to a multi-layer wall model for drug-eluting stents in which the zero-flux jump conditions and implicit concentration interface conditions are both present.