The utilization of high-energy composite propellants not only effectively enhances the energy performance of solid rocket motors (SRMs), but also aggravates the problem of combustion instability. Due to the typical microcosmic heterogeneous structure of composite propellants, slight changes in the propellant formulation can lead to significant differences in burning rates and combustion responses. The present work establishes an integrated combustion response model for four-component hydroxyl-terminated polybutadiene (HTPB) propellant with microcosmic heterostructure. The improved combustion model that considers the microstructure of four-component propellants is developed based on the heterogeneous quasi one-dimensional (HeQu1-D) framework, and the complex combustion process of composite propellant is simplified into a multi-modal particle geometry dominated by equivalent oxidizers. On the basis of the steady-state model, the unsteady burning of propellant is further considered to establish the relation between the steady-state burning rate and the transient burning rate according to the Zeldovich-Novozhilov solid-phase energy conservation. The model is well verified by comparing with experimental data, with a maximum error of 5.34 % in combustion response. Besides, the variations of content distribution and particle size are further investigated. The results demonstrate that adjusting the particle sizes of AP and NA can significantly alter the propellant's combustion response characteristics, where smaller AP particles combined with larger NA particles are more conducive to stable combustion. Regarding composition content, increasing the relative proportion of AP helps reduce the pressure-coupled response function of the propellant, while formulations with lower aluminum powder content exhibit better stability. When 10 % of AP is replaced with RDX, the pressure-coupled response function exhibits a peak value increase of 0.151 accompanied by a 25 Hz reduction in peak frequency. More pronounced effects are observed with HMX, where the same 10 % replacement leads to a greater peak value enhancement of 0.432 and a more substantial peak frequency decrease of 85 Hz. This work contributes to understanding the mechanism of combustion instability and provides guidance for efficient optimization of propellant formulations.