In industrial production, in order to maximize demand fulfillment with limited processing capacity, manufacturers introduce a mixed-model flexible flow line (MFFL), which allows concurrent processing of multiple SKUs and produces more products in both quantity and category. In this study, we develop an adaptive mixed-integer linear programming (MILP) scheduling model for the MFFL problem. The model captures two key constraints in industrial production: production continuity and process capability. For the MFFL problem, we also propose a five-level scheduling strategy that integrates on-time and in-full (OTIF), early production, late delivery, using safety stock, and finally cutting demand. The scheduling strategy and model are demonstrated by real cases with high efficiency. Interestingly, the proposed scheduling strategy and model also achieve machine load balancing in production. Furthermore, we explore the impact of production continuity and introduce alternative objective functions to reduce overproduction with acceptable increases in solving time. This study is helpful for manufacturers to satisfy the demand as much as possible under the constraint of processing capacity and the requirement of production continuity.