Authoring compelling animations often requires artists to come up with creative high-level ideas and translate them into precise low-level spatial and temporal properties like position, orientation, scale, and frame timing. Traditional animation tools offer direct manipulation strategies to control these properties but lack support for implementing higher-level ideas. Alternatively, AI-based tools allow animation production using natural language prompts but lack the fine-grained control over properties required for professional workflows. To bridge this gap, we propose AniMate, a hand-drawn animation system that integrates direct manipulation and natural language interaction. Central to AniMate are narrative motion blocks, clip-like components located on a timeline that let animators specify animated behaviors with a combination of textual and manual input. Through an expert evaluation and the creation of short demonstrative animations, we show how focusing on intermediate-level actions provides a common representation for animators to work across both interaction modalities.