An absorptive/transmissive frequency selective surface (ATFSS) with multiple transmission zeros is proposed, which consists of one lossy layer and two lossless layers separated by air space. As the key features, the slot-line loading and electromagnetic coupling technologies are adopted in the lossy layer and lossless layers, respectively, to introduce the infinite impedance points and four transmission zeros, thereby simultaneously achieving low insertion loss and high selectivity of the transmission band. Benefiting from the ohmic loss of the lumped resistance in the lossy layer, effective absorption can be readily implemented. A detailed qualitative analysis of the proposed structure is presented through the equivalent circuit theory, surface current, and power loss density distributions. Under normal incidence, the overall structure exhibits two discrete absorption bands over the frequency range of 6.34 to 13.40 GHz, whereas a transmission behavior is obtained from 9.34 to 11.40 GHz with a minimum insertion loss of only 0.14 dB. In particular, there are only 3.9% and 3% transition bandwidths between absorption and transmission functions. Then, a sample prototype is fabricated for demonstration, and the measured results are well consistent with the simulated one. As expected, the proposed ATFSS has the advantage of multiple transmission zeros, loss insertion loss, and narrow transition band, which is of great potential in the application of radar stealth radome.