Automated classification of breast cancer can often save lives, as manual detection is usually time-consuming & expensive. Since the last decade, deep learning techniques have been most widely used for the automatic classification of breast cancer using histopathology images. This paper has performed the binary and multi-class classification of breast cancer using a transfer learning-based ensemble model. To analyze the correctness and reliability of the proposed model, we have used an imbalance IDC dataset, an imbalance BreakHis dataset in the binary class scenario, and a balanced BACH dataset for the multi-class classification. A lightweight shallow CNN model with batch normalization technology to accelerate convergence is aggregated with lightweight MobileNetV2 to improve learning and adaptability. The aggregation output is fed into a multilayer perceptron to complete the final classification task. The experimental study on all three datasets was performed and compared with the recent works. We have fine-tuned three different pre-trained models (ResNet50, InceptionV4, and MobilNetV2) and compared it with the proposed lightweight ensemble model in terms of execution time, number of parameters, model size, etc. In both the evaluation phases, it is seen that our model outperforms in all three datasets.