The possibility of growth by the liquid phase epitaxy method of a new type of advanced composite scintillator based on Ce3+-doped single crystalline films (SCFs) of Lu1.5Gd1.5Al1.5Ga3.5O12 garnet and substrates from single crystals (SCs) of Gd3Al2.5Ga2.5O12:Ce garnet is evidenced for the first time in this work. We show the possibility of the simultaneous registration of α-particles and γ-quanta by way of separation of the scintillation pulse height spectra and decay kinetics of SCF and crystal parts of such a composite scintillator. Namely, the significant differences in the scintillation decay kinetics of Lu1.5Gd1.5Al1.5Ga3.5O12:Ce SCF/Gd3Al2.5Ga2.5O12:Ce SC composite scintillator under excitation by α-particles of a 241Am (5.5 MeV) source and γ-quanta of 137Cs (662 keV) source are observed. The respective tα/tγ decay times ratio in the 0-500 ns range reach up to 0.5 for this type of composite scintillator; e.g., the SCF scintillators is two times faster than the substrate scintillator. For this reason, such a type of composite scintillator can be successfully applied for the separation of the signals coming from its film and crystal parts at the registration of the mixed radiation fluxes of α-particles and γ-quanta.