Selection bias hinders recommendation models from learning unbiased user preference. Recent works empirically reveal that pursuing invariant user and item representation across biased and unbiased data is crucial for counteracting selection bias. However, our theoretical analysis reveals that simply optimizing representation invariance is insufficient for addressing the selection bias — recommendation performance is bounded by both representation invariance and discriminability. Worse still, current invariant representation learning methods in recommendation neglect even hurt the representation discriminability due to data sparsity and label shift. In this light, we propose a new Discriminative-Invariant Representation Learning framework for unbiased recommendation, which incorporates label-conditional clustering and prior-guided contrasting into conventional invariant representation learning to mitigate the impact of data sparsity and label shift, respectively. We conduct extensive experiments on three real-world datasets, validating the rationality and effectiveness of the proposed framework. Code and supplementary materials are available at: https://github.com/HungPaan/DIRL.