With regard to a solution problem of the interval-valued multiobjective cooperative games with payoffs of inclusion and/or overlap relations, the two-phase nonlinear programming models and method are proposed. In view of the multiobjective factors in the real decision problem, the relation of interval ranking and the concept of interval-valued cores of interval-valued multiobjective cooperative games based on the satisfactory degree are defined. Hereby, the multiobjective two-phase nonlinear programming solution models and corresponding bisection steps are proposed. Finally, the feasibility and applicability of the models and method are illustrated by a numerical example.