Surveillance facial images are often captured under unconstrained conditions, resulting in severe quality degradation due to factors such as low resolution, motion blur, occlusion, and poor lighting. Although recent face restoration techniques applied to surveillance cameras can significantly enhance visual quality, they often compromise fidelity (i.e., identity-preserving features), which directly conflicts with the primary objective of surveillance images -- reliable identity verification. Existing facial image quality assessment (FIQA) predominantly focus on either visual quality or recognition-oriented evaluation, thereby failing to jointly address visual quality and fidelity, which are critical for surveillance applications. To bridge this gap, we propose the first comprehensive study on surveillance facial image quality assessment (SFIQA), targeting the unique challenges inherent to surveillance scenarios. Specifically, we first construct SFIQA-Bench, a multi-dimensional quality assessment benchmark for surveillance facial images, which consists of 5,004 surveillance facial images captured by three widely deployed surveillance cameras in real-world scenarios. A subjective experiment is conducted to collect six dimensional quality ratings, including noise, sharpness, colorfulness, contrast, fidelity and overall quality, covering the key aspects of SFIQA. Furthermore, we propose SFIQA-Assessor, a lightweight multi-task FIQA model that jointly exploits complementary facial views through cross-view feature interaction, and employs learnable task tokens to guide the unified regression of multiple quality dimensions. The experiment results on the proposed dataset show that our method achieves the best performance compared with the state-of-the-art general image quality assessment (IQA) and FIQA methods, validating its effectiveness for real-world surveillance applications.