The ongoing debate on the ethics of using artificial intelligence (AI) in military contexts has been negatively impacted by the predominant focus on the use of lethal autonomous weapon systems (LAWS) in war. However, AI technologies have a considerably broader scope and present opportunities for decision support optimization across the entire spectrum of the military decision-making process (MDMP). These opportunities cannot be ignored. Instead of mainly focusing on the risks of the use of AI in target engagement, the debate about responsible AI should (i) concern each step in the MDMP, and (ii) take ethical considerations and enhanced performance in military operations into account. A characterization of the debate on responsible AI in the military, considering both machine and human weaknesses and strengths, is provided in this paper. We present inroads into the improvement of the MDMP, and thus military operations, through the use of AI for decision support, taking each quadrant of this characterization into account.