While learning embedding models has yielded fruitful results in several NLP subfields, most notably Word2Vec, embedding correspondence has relatively not been well explored especially in the context of natural language understanding (NLU), a task that typically extracts structured semantic knowledge from a text. A NLU embedding model can facilitate analyzing and understanding relationships between unstructured texts and their corresponding structured semantic knowledge, essential for both researchers and practitioners of NLU. Toward this end, we propose a framework that learns to embed semantic correspondence between text and its extracted semantic knowledge, called semantic frame. One key contributed technique is semantic frame reconstruction used to derive a one-to-one mapping between embedded vectors and their corresponding semantic frames. Embedding into semantically meaningful vectors and computing their distances in vector space provides a simple, but effective way to measure semantic similarities. With the proposed framework, we demonstrate three key areas where the embedding model can be effective: visualization, semantic search and re-ranking.