Over recent years, podcasts have emerged as a novel medium for sharing and broadcasting information over the Internet. Audio streaming platforms originally designed for music content, such as Amazon Music, Pandora, and Spotify, have reported a rapid growth, with millions of users consuming podcasts every day. With podcasts emerging as a new medium for consuming information, the need to develop information access systems that enable efficient and effective discovery from a heterogeneous collection of music and podcasts is more important than ever. However, information access in such domains still remains understudied. In this work, we conduct a large-scale log analysis to study and compare podcast and music search behavior on Spotify, a major audio streaming platform. Our findings suggest that there exist fundamental differences in user behavior while searching for podcasts compared to music. Specifically, we identify the need to improve podcast search performance. We propose a simple yet effective transformer-based neural instant search model that retrieves items from a heterogeneous collection of music and podcast content. Our model takes advantage of multi-task learning to optimize for a ranking objective in addition to a query intent type identification objective. Our experiments on large-scale search logs show that the proposed model significantly outperforms strong baselines for both podcast and music queries.