The Just Noticeable Difference (JND) reveals the minimum distortion that the Human Visual System (HVS) can perceive. Traditional studies on JND mainly focus on background luminance adaptation and contrast masking. However, the HVS does not perceive visual content based on individual pixels or blocks, but on the entire image. In this work, we conduct an interactive subjective visual quality study on the Picture-level JND (PJND) of compressed stereo images. The study, which involves 48 subjects and 10 stereoscopic images compressed with H.265 intra coding and JPEG2000, includes two parts. In the first part, we determine the minimum distortion that the HVS can perceive against a pristine stereo image. In the second part, we explore the minimum distortion that each subject perceives against a distorted stereo image. Modeling the distribution of the PJND samples as Gaussian, we obtain their complementary cumulative distribution functions, which are known as Satisfied User Ratio (SUR) functions. Statistical analysis results demonstrate that the SUR is highly dependent on the image contents. The HVS is more sensitive to distortion in images with more texture details. The compressed stereoscopic images and the PJND samples are collected in a data set called SIAT-JSSI, which we release to the public.