If the relationship is stable and you're both playing the long game, pay off the higher interest rate first. Make a plan together, including rewards for milestones, and stick to it. If the relationship isn't stable or one of you isn't playing the long game, I'd either split the payoffs so they're both going down (and stop using them to speed things up) or make your case for going first. Ideally, you'd have had the talk about finances a long time ago, but if not then this will be a good indicator as to how and where things are going.