•Propose integrated ATFM models for separation management and ground holding•Jointly consider system efficiency and inter-airline equity when allocating ATFM delay•Introduce robustness to both system efficiency and inter-airline equity•Develop exact, heuristic, and learning-augmented heuristic solution approaches•Propose three methods for solution selection from a Pareto frontier Motivated by a recent air traffic flow management (ATFM) initiative in the Southeast Asia region, this paper considers a new ATFM model that integrates Minutes-In-Trail (MINIT) with ground holding and jointly considers system efficiency and inter-airline equity. Three equity metrics are investigated including two Gini coefficient-based metrics previously not considered for inter-airline equity. We formulate both deterministic and robust bi-objective optimization models, with the notion of robustness introduced to equity as well as to efficiency. Several solution approaches are proposed, including an exact approach based on the ε-constraint method and linearization techniques, and heuristics approaches which adapt nondominated sorting genetic algorithm (NSGA-II) and a learning-augmented nondominated sorting move (L-NSM) algorithm. For solving the robust bi-objective models, Monte Carlo sampling is further integrated with L-NSM. As inter-airline equity is of primary concern in the models, we also propose three methods for solution selection from a Pareto frontier for potential ATFM use that take into account flight-level equity from different perspectives. Extensive numerical analysis is conducted showing superior performance of L-NSM in both computation time and solution quality for small, medium, and large cases, benefits of the proposed ATFM initiative over a case with only MINIT but no ground holding, differences and similarities of the three equity metrics used, characteristics of the selected solutions from Pareto frontiers using the three proposed methods, benefits of considering robustness, and results sensitivity to key parameters. Findings of this research shed lights on further development of integrated ATFM modeling of separation management with ground holding with bi-objective consideration and relevant practices.