Self-supervised learning (SSL) models have significantly advanced speech processing tasks, and several benchmarks have been proposed to validate their effectiveness. However, previous benchmarks have primarily focused on single-speaker scenarios, with less exploration of target-speaker tasks in noisy, multi-talker conditions -- a more challenging yet practical case. In this paper, we introduce the Target-Speaker Speech Processing Universal Performance Benchmark (TS-SUPERB), which includes four widely recognized target-speaker processing tasks that require identifying the target speaker and extracting information from the speech mixture. In our benchmark, the speaker embedding extracted from enrollment speech is used as a clue to condition downstream models. The benchmark result reveals the importance of evaluating SSL models in target speaker scenarios, demonstrating that performance cannot be easily inferred from related single-speaker tasks. Moreover, by using a unified SSL-based target speech encoder, consisting of a speaker encoder and an extractor module, we also investigate joint optimization across TS tasks to leverage mutual information and demonstrate its effectiveness.