H5P provides a very tight integration with Blackboard through H5P.com.
With H5P.com content may be created from within Blackboard, you get your own H5P content repository in Blackboard, and grades are stored in Blackboard. H5P.com also provides analytics within Blackboard so that teachers may see what the learners answered to the different questions within the H5P Content.
To get started with H5P in Blackboard just go to H5P.com and start a 30-day free trial. You should make sure your Blackboard admin is ready to set up the LTI integration.