With rapid advances in generative artificial intelligence, the text-to-music synthesis task has emerged as a promising direction for music generation. Nevertheless, achieving precise control over multi-track generation remains an open challenge. While existing models excel in directly generating multi-track mix, their limitations become evident when it comes to composing individual tracks and integrating them in a controllable manner. This departure from the typical workflows of professional composers hinders the ability to refine details in specific tracks. To address this gap, we propose JEN-1 Composer, a unified framework designed to efficiently model marginal, conditional, and joint distributions over multi-track music using a single model. Building upon an audio latent diffusion model, JEN-1 Composer extends the versatility of multi-track music generation. We introduce a progressive curriculum training strategy, which gradually escalates the difficulty of training tasks while ensuring the model's generalization ability and facilitating smooth transitions between different scenarios. During inference, users can iteratively generate and select music tracks, thus incrementally composing entire musical pieces in accordance with the Human-AI co-composition workflow. Our approach demonstrates state-of-the-art performance in controllable and high-fidelity multi-track music synthesis, marking a significant advancement in interactive AI-assisted music creation. Our demo pages are available at www.jenmusic.ai/research.