Reliably replicating the mechanical behavior of soft biological tissues using synthetic biomaterials remains a challenge in biomedical engineering. Hydrogels show promise due to their high water content, viscoelasticity, and adjustable stiffness; however, their lack of structural reinforcement limits their durability under cyclic loading their long-term mechanical stability in functional tissue models. This work presents the design and mechanical characterization of hydrogel-scaffold composites that combine a polyvinyl alcohol-based hydrogel [1] with additively manufactured 3D mesh structures. By embedding tailored mesh geometries into the hydrogel, the mechanical stability of the composite is enhanced while maintaining the compliant, hydrated nature of the hydrogel. This hybrid strategy also aims to reproduce the nonlinear and anisotropic stress-strain behavior characteristic of fiber-reinforced soft biological tissues. Experimental investigations involved sample preparation and cyclic compression-tension and shear testing of pure hydrogels and hydrogel-mesh composites. Reproducible sample geometries and controlled testing conditions enabled reliable comparisons across material formulations and scaffold architectures. The incorporation of 3D-printed meshes improved the composite stability and allowed tunable, direction-ependent mechanical responses governed by mesh design. To identify the key material and structural features governing the observed mechanical response, we used a probabilistic model discovery framework [2] that accounts for experimental uncertainty. This framework autonomously identifies dominant model terms and parameters directly from experimental data spanning multiple samples and loading modes. A Bayesian constitutive artificial neural network was trained to quantify the uncertainty of the discovered models for both the hydrogel-scaffold composite and its individual components. Posterior parameter distributions were inferred using Markov chain Monte Carlo sampling, while sparsity-promoting Bayesian priors were introduced to enhance robustness and interpretability and to avoid overfitting. Together, this data-driven and uncertainty-aware modeling approach enables an interpretable link between the design parameters of composite materials and their macroscopic mechanical behaviors, thereby supporting the development of mechanically robust, tissue-mimetic hydrogel systems.