Internal cooling and film cooling are two main cooling methods in modern gas turbines. They work together to protect the high-temperature components. This paper presents the results of a computational study on cooling performance for a flat plate with both film cooling and internal cooling using a conjugate heat transfer analysis. Three internal delivery channel geometries, smooth channel, channel roughened by square ribs, and channel roughened by crescent ribs, are studied with two film cooling geometries, cylindrical hole and sister holes. The respective conjugate cooling performances are compared. To help understand the interaction between film cooling and internal cooling, detailed flow and heat transfer characteristics are presented and discussed. Results show how overall cooling effectiveness is controlled by conjugate heat transfer of the two cooling schemes. Both film cooling effectiveness and internal cooling performance are influenced by the delivery channel geometry near the hole inlets. The sink flow effects of film cooling will enhance the heat transfer coefficient near the film cooling hole inlet, enhancing with stronger blowing ratio. At the same time, film cooling performance is affected by the internal channel as the flow inside the film cooling hole is influenced by the ribs near the hole inlets.