Multistage fractures in different reservoirs exhibit competitive extension and mutual feeding mechanisms under different fracturing sequence conditions. To better understand these mechanisms for a more efficient extraction of mine gases, a combination of true triaxial physical tests and numerical simulation was performed in this study. The expansion process of hydraulic fractures in different layers and the comprehensive effect of fracturing were analyzed. The directional deflection effect of the induced stress field on the hydraulic fractures can be summarized as follows. In terms of their behavioral pattern, the fractures in the rock seam extended “in the direction of maximum geo-stress and then deflected toward the interface.” The fracture behavior in the coal seams could be divided into two patterns: “deflection toward the interface and then extension along the direction of maximum geo-stress” and “deviation from the interface and then extension along the direction of maximum geo-stress.” The mutual feedback between the fractures manifested in the form of fracture “phase direction” in the case of stratified fracturing and “phase back” in the case of simultaneous fracturing, i.e., the fracture behaviors in the rock seams and in the first type of coal seams were promoted whereas the fracture behavior was inhibited in the second type of coal seams. In addition, the second fracturing process could be characterized by an increase in the fracture initiation pressure, a decrease in the rate of pressure drop, an increase in the fracture extension duration, and a decrease in the fracture width. When using a fracturing sequence of rock followed by coal, the formation of the seam network structure was found to be more favorable. When using a fracturing sequence of coal followed by rock, it was necessary to continue the injection of the hydraulic fluid into the first fracture during the second fracturing process, so as to obtain a higher fracturing yield. This research provides a certain theoretical support for the efficient co-exploitation of three gases, namely coalbed methane, tight gas, and shale gas, from coal composite reservoirs and in the prevention of gas disasters.