Metamaterial-based perfect absorbers utilize intrinsic loss, with the aid of appropriate structural design, to achieve near unity absorption at a certain wavelength. For most of the reported absorbers, the absorption occurs only at a single wavelength where plasmon resonances are excited in the nanostructures. Here we introduce a dual-band perfect absorber based on a gold nanocross structure. Two bands of maximum absorption of 94% are experimentally accomplished by breaking the symmetry of the cross structure. Furthermore, we demonstrate the two bands can be readily tuned throughout the mid-infrared with their associated resonances giving rise to large near-field enhancements. These features are ideal for multiband surface-enhanced infrared spectroscopy applications. We experimentally demonstrate this application by simultaneously detecting two molecular vibrational modes of a 4 nm thick polymer film utilizing our proposed absorber. Furthermore, in response to variations in the interaction strength between the plasmonic and molecular dipoles, we observe an anticrossing behavior and modification in the spectral line shape of the molecular absorption peak, which are characteristic of the coupling between the two modes.