This paper presents a joint model for performing unsupervised morphological analysis on words, and learning a character-level composition function from morphemes to word embeddings. Our model splits individual words into segments, and weights each segment according to its ability to predict context words. Our morphological analysis is comparable to dedicated morphological analyzers at the task of morpheme boundary recovery, and also performs better than word-based embedding models at the task of syntactic analogy answering. Finally, we show that incorporating morphology explicitly into character-level models helps them produce embeddings for unseen words which correlate better with human judgments.