Coproduction technology, whereby an original equipment manufacturer (OEM) and a third-party co-product manufacturer (CM) produce high-end and low-end products respectively by using different quality ranges of the same raw material, has been widely used. The CM who is in a disadvantaged position can hold strategic inventories to increase their bargaining power as the supply of raw materials is limited by the OEM. In this paper, we investigate the impact of the interaction between coproduction and strategic inventory on the profitability of OEMs and CMs as well as the overall performance of the supply chain. We model a two-stage game-theoretic framework in which the OEM acquires raw materials and uses a fraction of quality higher than the accepted standard to produce and sell a high-end product, and sells a low-end product through the CM to exploit the economic value of the remaining lower-quality raw materials, while the CM has the option to carry strategic inventories for two periods. We find that the presence of coproduction and strategic inventory (i.e., the CS case) occurs only when raw material cost is high and inventory holding cost is low. This leads to a significant increase in the production efficiency of low-end products compared to the case where no strategic inventory exists (i.e., the CN case). In addition, the negative impact of costs may lead to higher profits for OEMs and CMs even though it directly consumes their profits. The tradeoffs among market expansion, market shifting, competitive incentive, and differentiation incentive effects drive our findings.