This dataset supports the development and validation of machine learning interatomic potentials (MLIPs) for modeling hydrogen absorption in C14 (hexagonal) and C15 (cubic) TiCr₂-based Laves phases. It includes density functional theory (DFT) calculations, fitted moment tensor potentials (Level 16), and basin-hopping Monte Carlo (BHMC)-sampled structures across a range of hydrogen concentrations and configurations. The data is organized into several directories: database/ contains DFT-calculated energies, forces, and stresses for training (Training_db/) and independent test configurations (Test_db/); dilute_H_configurations/ provides low-concentration hydrogen structures in both C14 and C15 phases, featuring face-connected (1D) and edge-connected (2D) interstitial arrangements computed with DFT; MC_structures/ includes minimum-energy hydrogenated structures from BHMC simulations using the trained MLIPs, along with relaxed DFT configurations, 108-atom C14 structures excluded from training, and the structures from Makarova; and trained_MTPs/ contains the final fitted MLIPs for both C14 (C14.mtp) and C15 (C15.mtp) phases. The dataset captures key aspects of hydrogen behavior in Laves phases, such as interstitial site occupation, hydrogen-hydrogen interactions, and the predictive performance of the force fields, and is fully referenced in the accompanying manuscript and supplementary materials.