Optically transparent microwave absorbers have been widely reported for electromagnetic stealth applications over the past few years, but developing ultra-wideband absorbers with high angular stability remains challenging. In this work, an absorber comprising a double-layer polymethylpentene (TPX) block and indium tin oxide (ITO) films has been designed, fabricated, and measured, respectively. Firstly, an impedance layer with novel coupled hexagonal combined elements is exploited to achieve ultra-wideband absorption. Secondly, to provide the optimal reflection response for high angular incidences, the TPX block with the lower permittivity is initially employed in the compensation and substrate layers. Finally, the experimental results agreed with simulation ones illustrate the excellent performance is concurrently achieved, including a 90% absorption bandwidth within 2.53-8.94 (111.8%), high angular stability (60°), and the high light transmittance (70.7%).