Emotion is essential in spoken communication, yet most existing frameworks in speech emotion modeling rely on predefined categories or low-dimensional continuous attributes, which offer limited expressive capacity. Recent advances in speech emotion captioning and synthesis have shown that textual descriptions provide a more flexible and interpretable alternative for representing affective characteristics in speech. However, progress in this direction is hindered by the lack of an emotional speech dataset aligned with reliable and fine-grained natural language annotations. To tackle this, we introduce AffectSpeech, a large-scale corpus of human-recorded speech enriched with structured descriptions for fine-grained emotion analysis and generation. Each utterance is characterized across six complementary dimensions, including sentiment polarity, open-vocabulary emotion captions, intensity level, prosodic attributes, prominent segments, and semantic content, enabling multi-granular modeling of vocal expression. To balance annotation quality and scalability, we adopt a human-LLM collaborative annotation pipeline that integrates algorithmic pre-labeling, multi-LLM description generation, and human-in-the-loop verification. Furthermore, these annotations are reformulated into diverse descriptive styles to enhance linguistic diversity and reduce stylistic bias in downstream modeling. Experimental results on speech emotion captioning and synthesis demonstrate that models trained on AffectSpeech consistently achieve superior performance across multiple evaluation settings.