This paper presents Hybrid Embroidery, a framework for interactive fabrication that leverages computational methods to broaden the possibilities of the craft of embroidery. Combining embroidery techniques, generative design methods, computer vision and a computerized embroidery machine, we show how this framework elicits a variety of innovative fabrication experiences that emphasize open-ended exploration, improvisation and play. The paper documents this framework, a series of sample results, challenges and next steps. It further outlines some of its implications for supporting creative exploration through real-time and direct manipulation of materials and close human-machine interaction.