In response to global environment challenges, particularly in transportation, there is a growing demand for designs that not only meet structural performances but are also lightweight. To respond to this need, we focus on a coated structure with pores inside like bones. In this research, we propose a shape and topology optimization of coated porous structure using different material for the coating and the pores. The porous material characteristics are calculated by the homogenization method, and applied to the core of the coated structure. The shape optimization is realized using the vector-type H1 gradient method and is applied to the boundary of the macro structure, the micro-pores and the interface between the materials. Concurrently the topology optimization defines the layout the of the core using the scalar-type H1 gradient method. Under the volume and equilibrium equation constraints, the compliance is minimized to stiffen the coated structure. After formulating this design optimization problem as a distributed-parameter optimization problem, the sensitivity functions for shape and topology are derived using the Lagrange multiplier method, the material derivative method and the adjoint method. The derived sensitivity functions are applied to the vector and scalar types H1 gradient method to determine the optimal shape and topology of the coated porous structure. The both types of H1 gradient method serve, enabling the achievement of a smooth optimal external shape while concurrently addressing potential issues related to grayscale and checkerboard patterns, as well as reducing the objective function. The effectiveness of this method is demonstrated through several design examples.