A hybrid model has been performed for modelling the thermomechanical behaviour of assembly structures with thin layers. The proposed approach called MAX-FEM model combines the matched asymptotics expansions (MAE) strategy and the eXtended Finite Element Method (X-FEM) to solve mediums with heterogeneities as embedded thin layers. Generally, a large number of finite elements is needed to solve explicitly the behaviour problem of thin layers and their effect on the whole assembly structure. In this work, a transient thermomechanical analysis has then been carried out to analyse the behaviour of 2D structures containing brazed joints. The methodology consists of the construction of enrichment parameters with the \MAE\ technique and their integration into the X-FEM formulation. Correction matrices of stiffness and conductivity are then defined and integrated in the \FEM\ computation algorithm. The obtained results in terms of temperature, displacements and stress distributions using the new ‘MAX-FEM' \UEL\ subroutine have been compared to those given by the standard \FE\ method under implicit \ABAQUS\ code.