Multilayer radar absorbing material (MRAM) is composed by superimposing different dielectric material layers with various thicknesses for reducing the reflection of electromagnetic (EM) wave. In this study, a novel triple-objective optimisation scheme based on Pareto-integrated artificial bee colony (P-ABC) algorithm is presented for the fully-optimised design of four broad-band and broad-angle MRAMs (BB-MRAMs) at the most interested radar bands 2-8, 8-12, 12-18 and 2-18 GHz between the angle range of 0 degrees-60 degrees. Two objective functions depending on total reflections (TRs) with TE and TM polarisations are constituted by taking the weighted mean of the TR in the incident wave angle and frequency. The BB-MRAMs are optimally designed by determining simultaneously the design variables of the thickness and material of each layer for minimising synchronously the three objective functions TE-TR, TM-TR and total thickness through the P-ABC, as well as by assuring the trade-off among the objectives. The BB-MRAMs are also verified under various cases through a comparison with simulated results by a full-wave simulator. The designed BB-MRAMs are even compared with the near-optimal MRAMs reported elsewhere. Therefore, the fully-optimised BB-MRAMs by the proposed triple-objective scheme are the global optimal designs thanks to the robust P-ABC algorithm.