Adhesive bonding has emerged as an attractive solution for the joining of lightweight structures, yet accurate stress analysis remains computationally demanding when relying on Finite Elements (FE). This paper introduces a novel plate Macro-Element (ME) formulation that extends previous beam-type approaches to enable three-dimensional stress analysis of bonded joints. High-order polynomial expansions are employed to describe the displacement field of the adherends, while the adhesive is modeled as an elastic foundation. Governing equations are derived using a variational principle and integrated within a standard FE framework. Through the derivation of a special stiffness matrix, a ME can simulate an entire overlap with just one element. The proposed methodology is validated against FE results for a single-lap bonded joint with a thin adhesive layer. The influence of different higher-order displacement assumptions and constitutive models is investigated. The results show that their inclusion in the formulation improves the solution accuracy.