Internal cooling and film cooling, as two main cooling methods in modern gas turbines, work together to protect the high-temperature components of gas turbines. 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 (SR), and channel roughened by crescent ribs (CR), are studied with two film cooling geometries, cylindrical hole, and sister holes (SS). The respective conjugate cooling performances are compared. Detailed flow and heat transfer characteristics are presented and discussed. Results show that both film cooling effectiveness and internal cooling performances are influenced by the delivery channel geometry near the hole inlets. The sink flow effects of film cooling enhance the heat transfer coefficient near the film cooling hole inlet. 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. When using sister holes, ribs in the internal channels make the anti-kidney vortex structure created by sister holes more effective by changing the mass flow distribution among the three holes.