Household financial planning requires simultaneous consideration of short-term liquidity, debt burden, long-term goals, risk-bearing capacity, and the prioritization of competing financial actions. Existing digital financial tools often treat these elements separately, while artificial-intelligence-based financial advisory systems introduce additional concerns regarding opacity, trust, and the traceability of recommendations. This study proposes the Explainable Multi-Index Financial Decision Framework (EMFDF), which integrates a Financial Health Index (FHI), Goal-Gap Index (GGI), Risk Capacity Index (RCI), and Financial Action Priority Score (FAPS) within a rule-constrained recommendation architecture. The framework is developed using a design science research orientation and evaluated through scenario-stratified synthetic household simulation. A total of 1,000 synthetic household profiles were generated to represent six decision contexts: emergency-fund inadequacy, excessive debt burden, insurance protection gaps, education-funding gaps, retirement-funding gaps, and long-term investment readiness. The deterministic recommendation engine achieved 92.7% agreement with the scenario benchmark. A random-forest surrogate model trained on the framework outputs achieved 89.0% holdout fidelity/accuracy, macro-precision of 0.888, macro-recall of 0.904, macro-F1 of 0.893, and macro-AUC of 0.988. Monotonicity tests confirmed that increases in emergency-fund adequacy did not reduce FHI, whereas increases in debt-service burden did not improve FHI. SHAP analysis identified the overall goal gap, debt-service ratio, education gap, emergency-fund adequacy, and retirement gap as the dominant drivers of model recommendations. The results demonstrate the internal coherence, transparency, and technical feasibility of the proposed framework as a proof-of-concept decision-support artifact. The study contributes a modular method for integrating household financial resilience, goal-based planning, risk capacity, constrained prioritization, and explainable machine learning. External validation using real households and professional financial planners is required before the framework can be interpreted as clinically or commercially validated financial advice.