We designed a composite both-sides-open disk resonator (CBSODR) structure by alternately arranging two types of BSODRs in a square lattice array. The simulation spectra of CBSODR structure showed two transmission peaks split by a sharp phase resonance (PR) dip with high quality factor. Previously developed PR structures based on Fabry–Perot resonance require a trade-off between resonant frequency and structural thickness. In contrast, we examined the mechanism underlying the PR effect induced by the CBSODR array by varying the diameters of the BSODR holes. We analyzed the PR effect by calculating the pressure and velocity fields of the CBSODR and further investigated the relationship between the operating frequency and geometric parameters. We could tune the resonant frequencies of the CBSODR structure while maintaining its thinness. We also applied the structure in a 1-propanol liquid concentration sensor. The results indicated a significant improvement in the sensor's figure of merit, which could be because the quality factor of the PR dip was high. At last, the experiment results showed the verification of the PR effect in CBSODR structure. The proposed CBSODR structure can be applied in underwater acoustic sensors and acoustic filters.