A Direct Sampling Method for Simultaneously Recovering Electromagnetic Inhomogeneous Inclusions of Different Nature

•Propose a DSM to simultaneously recover the support of inhomogeneities of different physical nature.•The DSM applies to highly limited data, even with only one or two sets of noisy measurement data.•The DSM is completely parallel, easy to implement, and fast to compute.•Two families of probing functions are constructed to improve the accuracy of reconstruction in different directions.•Theoretical justifications and extensive numerical experiments are conducted.