Using Molecular Dynamics Phonon Wave Packet Simulations, We Study Phonon Transmission Across Hexagonal (H)-BN and Amorphous Silica (A-SiO2) Nanoscopic Thin Films Sandwiched by Two Crystalline Leads. Due to the Phonon Interference Effect, the Frequency-Dependent Phonon Transmission Coefficient in the Case of the Crystalline Film (Si|h-BN|Al Heterostructure) Exhibits a Strongly Oscillatory Behavior. in the Case of the Amorphous Film (Si|a-SiO2|Al and Si|a-SiO2|Si Heterostructures), in Spite of Structural Disorder, the Phonon Transmission Coefficient Also Exhibits Oscillatory Behavior at Low Frequencies (Up to ∼1.2 THz), with a Period of Oscillation Consistent with the Prediction from the Two-Beam Interference Equation. above 1.2 THz, However, the Phonon Interference Effect is Greatly Weakened by the Diffuse Scattering of Higher-Frequency Phonons within an A-SiO2 Thin Film and at the Two Interfaces Confining the A-SiO2 Thin Film.