<p>Modeling extreme precipitation and temperature is vital for understanding the impacts of climate change, as hazards like intense rainfall and record-breaking temperatures can result in severe consequences, including floods, droughts, and wildfires. Gaining insight into the spatial variation and interactions between these extremes is critical for effective risk management, early warning systems, and informed policy-making. However, challenges such as the rarity of extreme events, spatial dependencies, and complex cross-variable interactions hinder accurate modeling. We introduce a novel framework for modeling spatial extremes, building upon spatial generalized extreme value (GEV) models. Our approach incorporates a dimension-reduced latent spatial process to improve flexibility and scalability, particularly in capturing asymmetry in cross-covariance structures. This joint latent spatial GEV model (JLS-GEV) overcomes key limitations of existing methods by providing a more flexible framework for inter-variable dependencies. In addition to addressing the rarity of extreme events, spatial dependence, and cross-variable interactions, JLS-GEV supports nonstationary spatial behaviors and independently collected data sources, while remaining computationally efficient through dimension reduction. We validate JLS-GEV through extensive simulation studies, demonstrating its superior performance in capturing spatial extremes compared to baseline modeling approaches. Application to real-world data on extreme precipitation and temperature in the southeastern USA highlights its practical utility. While primarily motivated by environmental challenges, this framework is broadly applicable to interdisciplinary studies of spatial extremes in interdependent natural processes. Supplementary materials accompanying this paper appear on-line.</p>