Multiband one-way polarization conversion and strong asymmetry in transmission inspired by it are demonstrated in ultrathin sandwiched structures that comprise two twisted aperture-type arrays of complementary split-ring resonators (CSRRs), metallic mesh, and dielectric layers. The basic features of the resulting mechanism originate from the common effect of chirality and tunneling. The emphasis is put on the (nearly) perfect polarization conversion of linear incident polarization into the orthogonal one and related diodelike asymmetric transmission within multiple narrow bands. Desired polarization conversion can be obtained at several resonances for one of the two opposite incidence directions, whereas transmission is fully blocked for the other one. The resonances, at which the (nearly) perfect conversion takes place, are expected to be inherited from similar structures with parallel, i.e., not rotated CSRR arrays that do not enable chirality and, thus, polarization conversion. It is found that the basic transmission and polarization conversion features and, thus, the dominant physics are rather general, enabling efficient engineering of such structures. The lowest-frequency resonance can be obtained in structures made of conventional materials with total thickness less than λ?/ 50 and up to ten such resonances can correspond to thickness less than λ ?/ 20 . ©2015 Optical Society of America.