The characterization and modeling of the out-of-plane behavior of fiber-based materials is essential for understanding their mechanical properties and improving their performance in various applications, especially in the forming process. Despite this, research on paper and paperboard has mainly focused on its in-plane behavior rather than its out-of-plane behavior. However, for accurate material characterization and modeling, it is critical to consider the out-of-plane behavior. In particular, delamination occurs during forming processes such as creasing, folding, and deep drawing. In this study, three material models for paperboard are presented: a single all-material continuum model and two composite models using different cohesion methods. The two composite models decouple in-plane and out-of-plane behavior and consist of continuum models describing the behavior of individual layers and cohesive interface models connecting the layers. Material characterization experiments are performed to derive the model parameters and verify the models. The models are validated using three-point bending and bulge tests and show good agreement. A case study is also conducted on the application of the three models in the simulation of a deep drawing process with respect to wrinkle formation. By comparing the simulation results of wrinkle formation in the deep drawing process, the composite models, especially the cohesive interface composite model, show greater accuracy in replicating the experimental results, indicating that a single continuum model can also be used to represent wrinkles.