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Whether hydraulic fractures could connect multiple gas zones in the vertical plane is the key to fracturing treatment to jointly exploit coalbed methane and tight sandstone gas through integrative hydraulic fracturing in tight sandstone–coal interbedded formations. Laboratory true triaxial hydraulic fracturing experiments were conducted on layered specimens with different combination types of natural sandstone and coal to simulate the propagation behavior of hydraulic fractures. The effects of the fracture initiation position, fracturing fluid viscosity and injection rate were discussed. The results showed that different fracture morphologies could be found. When initiating from coal seams, three patterns of fracture initiation and propagation were obtained: (1) The main hydraulic fracture initiated and propagated along the natural fractures and then diverged due to the effects of in situ stress and formed secondary fractures. (2) The hydraulic fracture initiated and propagated in the direction of the maximum horizontal stress. (3) Multiple fractures initiated and propagated at the same time. With the same fracturing fluid viscosity and injection rate, the hydraulic fractures initiating in sandstones had greater chances than those in coal seams to penetrate interfaces and enter neighboring layers. Excessively small or large fracturing fluid viscosity and injection rate would do harm to the vertical extension height of the induced fracture and improvement of the stimulated reservoir volume. Compared with operation parameters (fracturing fluid viscosity and injection rate), the natural weak planes in coals were considered to be the key factor that affected the fracture propagation path. The experimental results would make some contributions to the development of tight sandstone–coal interbedded reservoirs.