In order to broaden the absorbing bandwidth of radar-absorbing materials (RAMs), a type of sandwich-structure RAMs (SSRAMs) derived from a Salisbury absorber and comprising two dielectric layers and one resistive sheet was investigated. In this paper, the impedance characteristics of the SSRAMs were analysed and the mechanisms of broadening microwave-absorbing bandwidth were interpreted using a Smith chart. In order to realise the study’s SSRAMs, plain-woven glass fibre fabric and silicon carbide (SiC) fibre fabric with low electrical resistivity were employed as reinforcements of the dielectric layers and lossy layer, respectively. The microwave-absorbing properties of the SSRAMs were measured and compared with simulated results. The results showed that the experimental and simulated results were in good agreement, that the SSRAMs had better wideband microwave-absorbing properties and that the microwave-absorbing bandwidth at reflectivity below −10 dB can reach 11.6 GHz.