A crucial element in the diagnosis of breast cancer is the utilization of a classification method that is efficient, lightweight, and precise. Convolutional neural networks (CNNs) have garnered attention as a viable approach for classifying histopathological images. However, deeper and wider models tend to rely on first-order statistics, demanding substantial computational resources and struggling with fixed kernel dimensions that limit encompassing diverse resolution data, thereby degrading the model’s performance during testing. This study introduces BCHI-CovNet, a novel lightweight artificial intelligence (AI) model for histopathological breast image classification. Firstly, a novel multiscale depth-wise separable convolution is proposed. It is introduced to split input tensors into distinct tensor fragments, each subject to unique kernel sizes integrating various kernel sizes within one depth-wise convolution to capture both low- and high-resolution patterns. Secondly, an additional pooling module is introduced to capture extensive second-order statistical information across the channels and spatial dimensions. This module works in tandem with an innovative multi-head self-attention mechanism to capture the long-range pixels contributing significantly to the learning process, yielding distinctive and discriminative features that further enrich representation and introduce pixel diversity during training. These novel designs substantially reduce computational complexities regarding model parameters and FLOPs, which is crucial for resource-constrained medical devices. The outcomes achieved by employing the suggested model on two openly accessible datasets for breast cancer histopathological images reveal noteworthy performance. Specifically, the proposed approach attains high levels of accuracy: 99.15 % at 40× magnification, 99.08 % at 100× magnification, 99.22 % at 200× magnification, and 98.87 % at 400× magnification on the BreaKHis dataset. Additionally, it achieves an accuracy of 99.38 % on the BACH dataset. These results highlight the exceptional effectiveness and practical promise of BCHI-CovNet for the classification of breast cancer histopathological images.