Mule provides options for integrating with Java Message Service (JMS) for asynchronous, reliable messaging between applications. JMS can be used with queues and topics to send and receive messages containing various payloads like strings, objects, and streams. Mule works with external JMS implementations like ActiveMQ rather than providing its own server. It supports various JMS specifications and allows configuration of connectors, endpoints, message types, durable subscriptions, and filters to integrate with different JMS brokers.