Micro-perforated panel absorbers can typically achieve either visual transparency or broadband absorption, but not both. This paper assesses the potential of Multilayer Micro-Slit panels to maintain both of these characteristics simultaneously. Micro-slit panels are similar to micro-perforated panels, and can similarly achieve high absorption coefficients without fibrous backing materials. The arrangement of slits are better suited to visual transparency than perforated holes because it provides more unobstructed panel per perforated area. However, these types of absorbers are limited to a narrow frequency bandwidth of effective absorption. By combining several panels into a multilayer assembly, broadband absorption becomes possible. The inherent complexity stemming from optimizing the parameters for multiple layers to meet a given design criteria necessitates the use of the Bayesian framework. This probabilistic method rapidly hones in on the best parameters of each individual layer so that the overall composite meets the design goal. Furthermore, Bayesian inference implemented cyclically alongside panel fabrication and testing allows for corrections of fabrication tolerances while assessing visual transparency.