The trend toward increasing energy efficiency and variable renewable energy (VRE) production has implications for combined heat and power (CHP) plants, which operate in both the price-driven power market and the district heating (DH) sector. Since CHP will be important in VRE integration, we develop a complementarity model to analyze CHP producers' roles in integrated markets. We use a Nordic case study to gain insights into (i) the effect of the link between CHP and DH on market power and (ii) market power's impact on operations in the DH sector. The results indicate that (i) the link of CHP to DH supply can increase market power and (ii) market power can induce shifts in DH production from heat-only to CHP.