The combustion response of solid propellants plays a crucial role in determining the combustion stability of solid rocket motors (SRMs). This study employs multiple advanced combustion diagnostic techniques, including high-speed photomicrography, two-color pyrometry, and laser shadowgraphy, to simultaneously capture mesoscale flame dynamics and burning surface regression characteristics of AP/HTPB composite propellants under pressure oscillations. This experimental configuration enables the simultaneous achievement of high temporal resolution (0.25 ms) and spatial resolution (4.9μm/pixel). Pressure oscillations are generated by loudspeakers, cover a range of frequencies (168.9 Hz to 506.7 Hz) and amplitudes up to approximately 0.44% of the equilibrium pressure. The investigated propellants exhibit varying oxidizer characteristics, including coarse (330μm) and fine (150μm) AP particle sizes, as well as different AP mass fractions (81% and 86%). Results reveal that finer oxidizer particles and higher oxidizer content both result in an increased mean steady burning rate, with the former exhibiting a more pronounced influence on the burning rate increment. Under pressure oscillations, the mean burning rate increases with increasing pressure oscillation amplitude, accompanied by a reduction in flame height, an expansion in mean flame swing angle, and an elevation in mean flame temperature. The observed frequency dependency indicates a stronger combustion response when the oscillation frequency aligns with the characteristic frequency of propellant, which is closely associated with the mean burning rate, irrespective of the amplitude of pressure oscillation. This frequency-dependent phenomenon results in the highest combustion response, characterized by a maximum mean burning rate increment exceeding 165%. The innovative experimental platform employed in this study demonstrates the capability to simultaneously capture various flame fluctuation characteristics, such as flame swinging, flame temperature, and burning rate fluctuation in a single test. This facilitates a more thorough and comprehensive analysis of combustion responses in solid propellants under pressure oscillations.