We theoretically study the metal-insulator-metal (MIM) structure based ultrathin broadband optical absorber which consists of a metallic substrate, a dielectric middle layer, and a nanostructured metallic top layer. It is found that, there exists an effective permittivity, εnull, for the top nanostructured metallic layer which leads to unit-absorption (zero-reflection) of the MIM structure. Importantly, this εnull exhibits abnormal dispersion behaviors. Both its real and imaginary parts increase monotonically with the wavelength. To obtain such naturally non-existing permittivity, we investigate the optical properties of two typical types of metal-dielectric nanocomposites, namely, thoroughly mingled composites using Bruggeman's effective medium theory, and more realistic Au nanosphere-in-dielectric structures using numerical permittivity retrieval techniques. We demonstrate that the εnull-type dispersions, and consequently, perfect absorption can be obtained over a broad spectral range when the filling factor of the metal component is close to the percolation threshold. The result not only explains the recently reported broadband absorbers made of randomly deposited Au nanoparticles [M. K. Hedayati, et al, Adv. Mater. 23, 5410 (2011)], but also provides theoretical guidelines for designing ultrathin broadband plasmonic absorbers for a wealthy of important applications.