Microbolometer arrays, i.e., arrays of micro-scale pixels sensing temperature via resistance changes, have proven to be an effective basis for real-time imaging instrumentation in infrared as well as terahertz frequencies. In previous work, a design of THz and IR absorbing nano-laminates of dielectric and metal layers was studied. It was shown via numerical modeling that absorption may be maximized by appropriate choices of thickness, permittivity and conductivity. In this work, an analytical approach to the problem is formulated based on the standard recursive multiple reflection formulas for multi-layered planar structures. The results fully confirm and extend previous numerical work. A previous relationship between wavelength and silicon thickness for maximum absorption, derived numerically for specific parameter combinations, is now generalized in a parametric closed form. The method can be extended to include multiple lossy dielectric layers and may serve as a tool for optimizing the absorption characteristics of more complex layered absorbing structures. This could enhance the sensitivity of the detection scheme of interest, providing benefits in terms of cost, efficiency, precision, and adjustability.