Breast ultrasound is useful for the diagnosis of breast tumors which can be benign or malignant. However, accurate segmentation of breast tumors and the classification of breast ultrasound into benign, malignant, or normal (no tumor) categories is challenging because of different reasons including poor contrast of the tumor region and absence of clear margins. We propose a Multibranch UNet architecture that uses multitask learning for the automated segmentation of breast tumors and classification of breast ultrasound images. Our model exploits the principle of autoencoding to achieve the aforementioned goals by utilizing salient image features. Experiments on publicly available datasets shows the superiority of our model over several state-of-the-art approaches.