Metamaterial perfect absorbers (MPAs) show great potential in achieving exceptional sensing performance, particularly in the realm of surface-enhanced infrared absorption (SEIRA) spectroscopy. To this aim, it is highly desirable for the localized hotspots to be readily exposed and accessible to analyte with strong mode confinement to enhance absorption. Here, we propose a quasi-three-dimensional MPA based on cross-shaped coupled complementary plasmonic arrays for highly sensitive refractive index sensing and molecular vibrational sensing. Dual-band perfect absorption can be approached with the two plasmonic resonances corresponding to the electric dipole-like mode of cross antenna array and the magnetic dipole-like mode of cross hole array, respectively. Large portions of the electric field of the hotspots are exposed and concentrated in the gap between the elevated cross antenna and its complementary structure on the substrate, leading to improved sensing sensitivities. An ultrathin polymethyl methacrylate (PMMA) film induces a significant redshift of the magnetic dipole-like mode with an 11.8 nm resonance shift per each nanometer polymer thickness. The value is comparable to the reported sensitivity of single molecule layer sensors. Additionally, the simultaneous detection of the C = O and C-H vibrations of PMMA molecules is enabled with the two plasmonic resonances adjusted by changing the lengths of the two cross branches. Remarkably, the observed mode splitting and anti-crossing behavior imply the strong interaction between plasmonic resonance and molecular vibration. Our dual-band MPA based on coupled complementary plasmonic arrays opens a new avenue for developing highly sensitive sensors for the detection of refractive index and multispectral molecular vibrations.