The depletion of producing layers leads to significant stress changes in adjacent targets, especially when complex natural fractures are present. Due to weak bedding interfaces or small stress barriers, hydraulic fractures can easily penetrate neighboring layers, and this further increases the chance of multilayer stress disturbance. In this work, we investigate the effects of vertical fracture complexity, i.e., hydraulic fracture penetration and interlayer natural fracture existence, on stress interference between different layers using a data set from a typical shale gas well in the Sichuan Basin. Two geological contexts, i.e., without interlayer natural fractures (w/o INF) and with interlayer natural fractures (w/ INF), are considered under different degrees of fracture penetration and interlayer connectivity. An in-house iteratively coupled geomechanics and compositional reservoir simulator is used to model the three-dimensional pressure and stress changes. The non-uniform hydraulic fractures and stochastic natural fractures are incorporated in our coupled simulation with an embedded discrete fracture model (EDFM). Comprehensive spatial-temporal stress analysis quantifies the approximate range of orientation change of SHmax and magnitude change of Shmin under various reservoir conditions. Numerical results indicate that the presence of natural fractures in the interlayer upgrades the risk of stress interference between different pay zones. A larger hydraulic fracture penetration increases gas production, but also exerts a significant impact on stress reorientation and redistribution in the upper potential layer. The orientation change of SHmax along the prospective infill location is below 10 degrees in the w/o INF cases but up to 30 degrees in the w/ INF cases with a moderate number of interlayer natural fractures. The average magnitude change of Shmin is within 3.5 MPa along the prospective infill location for most w/o INF cases, whereas that in the w/ INF cases is above 10 MPa at most times. Moreover, the existence of natural fractures in the interlayer brings forward the occurrence of maximum orientation change in the upper layer by around one year. While inducing non-negligible stress drop in the upper layer, higher interlayer matrix permeability does not significantly reorient the horizontal principal stresses. Varying the density of interlayer natural fractures not only affects the stress magnitude but also causes considerable orientation change in the upper layer. The findings from this work help understand the extent of stress interference in the upper potential layer of the Sichuan Basin under different vertical fracture complexities. It is of guiding significance for future hydraulic fracture design and child-well operations in similar highly fractured tight formations.