Carbon cap-and-trade and carbon offsets are common and important carbon emission reduction policies in many countries. In addition, carbon emissions from business activities can be effectively reduced through specific capital investments in green technologies. Nevertheless, such capital investments are costly and not all enterprises can afford these investments. Therefore, if all members of a supply chain agree to share the investments in the facilities, the supply chain can reduce carbon emissions and generate more profit. Under carbon cap-and-trade and carbon tax policies, this study proposes a production–inventory model in which the buyer and vendor in the integrated supply chain agree to co-invest funds to reduce carbon emissions. We planned to integrate production, delivery, replenishment, and technology to reduce carbon emissions so as to maximize the total profit of the supply chain system. Several examples are simulated and the sensitivity analysis of the main parameters is carried out. The optimal solutions and joint total profit under various carbon emission policies are also compared. The future carbon emission control trend is expected to enable companies to share risks by co-investing and developing sustainable supply chains.