In this paper, we study the effective thermo-elastic properties of hybrid materials containing layered auxetic microstructures. We consider three types of arrangements: (1) hybrids with randomly distributed plate-like inclusions possessing the negative Poisson's ratio and negative thermal expansion coefficient, (2) sandwich structures with auxetic cores and (3) laminates with randomly arranged and ordered auxetic and negative thermal expansion layers. We evaluate the effective characteristics of these hybrids by analysing representative volume elements using the finite element method. We observe that the plate-like auxetic inclusions increase the effective stiffness of the hybrid. This stiffening effect was previously reported for spherical and cubic auxetic inclusions and is further investigated in this study. We demonstrate that the aspect ratio of the plate-like shapes has strong influence on this stiffening effect: the decrease in the aspect ratio reduces stiffening in the direction parallel to the layers and enhances it in the direction perpendicular to them. In the auxetic laminates, the stiffening effect strengths with the increase in the number of auxetic layers. We also show that thinner inclusions provide lower effective linear coefficient of thermal expansion (CTE) in the direction parallel to the layering and higher effective CTE in the direction perpendicular to it.