We present a unified model capable of simultaneously grounding both spoken language and non-speech sounds within a visual scene, addressing key limitations in current audio-visual grounding models. Existing approaches are typically limited to handling either speech or non-speech sounds independently, or at best, together but sequentially without mixing. This limitation prevents them from capturing the complexity of real-world audio sources that are often mixed. Our approach introduces a ``mix-and-separate'' framework with audio-visual alignment objectives that jointly learn correspondence and disentanglement using mixed audio. Through these objectives, our model learns to produce distinct embeddings for each audio type, enabling effective disentanglement and grounding across mixed audio sources. Additionally, we created a new dataset to evaluate simultaneous grounding of mixed audio sources, demonstrating that our model outperforms prior methods. Our approach also achieves state-of-the-art performance in standard segmentation and cross-modal retrieval tasks, highlighting the benefits of our mix-and-separate approach.