I think you should check this documentation. There is option for creating custom traces related to WebJobs:
Hey Sebastian -
We figured that azure function functionality would eventually be able to help us - but when we were evaluating (positively!) we discovered that the one agent was not seeing methods that we knew were being fired inside our WebJobs.
I dont have access to a system to repeat this with the latest bits yet - but we will be doing so once we start using Dynatrace again.
One of the issues is that our WebJobs are not HTML Triggered - they run as batch on the Application Services as WEB JOBS.
Yeah - thats what we thought too. We were able to instrument just about everything - but the webjobs seemed to be unavailable to the agent.
We think this has to do with how they are hosted: they execute in their own process space, and are homed in a directory that makes them look like a service extension (this can make deployments with app services with extensions very complicated...) - also If you turn off an app service the webjobs can continue to execute (this is a really terrible thing)
I also spent a lot of time saying "webjob" and having people not understand what I was talking about so we figured we would wait until we were a paying customer and then participate in some mutual education.