Improving the greenness and conformance quality of a product is two fundamental and intertwined considerations in today's supply chain decision-making. However, the related literature rarely considers conformance quality improvement of products in green supply chain management. This paper incorporates both into a framework to analyze the optimal strategies of a manufacturer responsible for conformance quality of product and greenness improvement and a retailer responsible for product marketing in a supply chain under four contracts: full cooperation, price-only contract, two-part tariff, and marketing cost-sharing. The analysis shows that full cooperation and two-part tariffs lead to the same and highest product quality, greenness, overall profit, and social welfare, but full cooperation is difficult to achieve in the supply chain. For the profit-maximizing manufacturer and retailer, the manufacturer most prefers two-part tariff contracts while the retailer prefers marketing cost-sharing because both achieve the highest profit in the preferred contract. Under the price-only contract, conformance quality of product and greenness are lowest, and profit levels for manufacturers and retailers are lowest. In all four cases, increased environment and quality awareness contribute to improved product greenness and conformance quality, leading to higher profits for the manufacturer and retailer and higher social welfare.