Adversarial attacks on Face Recognition (FR) systems have proven highly effective in compromising pure FR models, yet adversarial examples may be ineffective to the complete FR systems as Face Anti-Spoofing (FAS) models are often incorporated and can detect a significant number of them. To address this under-explored and essential problem, we propose a novel setting of adversarially attacking both FR and FAS models simultaneously, aiming to enhance the practicability of adversarial attacks on FR systems. In particular, we introduce a new attack method, namely Style-aligned Distribution Biasing (SDB), to improve the capacity of black-box attacks on both FR and FAS models. Specifically, our SDB framework consists of three key components. Firstly, to enhance the transferability of FAS models, we design a Distribution-aware Score Biasing module to optimize adversarial face examples away from the distribution of spoof images utilizing scores. Secondly, to mitigate the substantial style differences between live images and adversarial examples initialized with spoof images, we introduce an Instance Style Alignment module that aligns the style of adversarial examples with live images. In addition, to alleviate the conflicts between the gradients of FR and FAS models, we propose a Gradient Consistency Maintenance module to minimize disparities between the gradients using Hessian approximation. Extensive experiments showcase the superiority of our proposed attack method to state-of-the-art adversarial attacks.