In modern recommendation systems, unbiased learning-to-rank (LTR) is crucial for prioritizing items from biased implicit user feedback, such as click data. Several techniques, such as Inverse Propensity Weighting (IPW), have been proposed for single-sided markets. However, less attention has been paid to two-sided markets, such as job platforms or dating services, where successful conversions require matching preferences from both users. This paper addresses the complex interaction of biases between users in two-sided markets and proposes a tailored LTR approach. We first present a formulation of feedback mechanisms in two-sided matching platforms and point out that their implicit feedback may include position bias from both user groups. On the basis of this observation, we extend the IPW estimator and propose a new estimator, named two-sided IPW, to address the position bases in two-sided markets. We prove that the proposed estimator satisfies the unbiasedness for the ground-truth ranking metric. We conducted numerical experiments on real-world two-sided platforms and demonstrated the effectiveness of our proposed method in terms of both precision and robustness. Our experiments showed that our method outperformed baselines especially when handling rare items, which are less frequently observed in the training data.