This paper addresses the problem of generating 3D interactive human motion from text. Given a textual description depicting the actions of different body parts in contact with objects, we synthesize sequences of 3D body poses that are visually natural and physically plausible. Yet, this task poses a significant challenge due to the inadequate consideration of interactions by physical contacts in both motion and textual descriptions, leading to unnatural and implausible sequences. To tackle this challenge, we create a novel dataset named RICH-CAT, representing ``Contact-Aware Texts'' constructed from the RICH dataset. RICH-CAT comprises high-quality motion, accurate human-object contact labels, and detailed textual descriptions, encompassing over 8,500 motion-text pairs across 26 indoor/outdoor actions. Leveraging RICH-CAT, we propose a novel approach named CATMO for text-driven interactive human motion synthesis that explicitly integrates human body contacts as evidence. We employ two VQ-VAE models to encode motion and body contact sequences into distinct yet complementary latent spaces and an intertwined GPT for generating human motions and contacts in a mutually conditioned manner. Additionally, we introduce a pre-trained text encoder to learn textual embeddings that better discriminate among various contact types, allowing for more precise control over synthesized motions and contacts. Our experiments demonstrate the superior performance of our approach compared to existing text-to-motion methods, producing stable, contact-aware motion sequences. Code and data will be available for research purposes.