Hi,
Thanks for using our plugins. I can help out.
We do not have a feature to display both the Month and List view on the same page.
You can use the themer’s guide to modify the Month View Template:
https://theeventscalendar.com/knowledgebase/themers-guide/
You could then add a custom query to show a list view under the month view or you could use a plugin such as the Event Rocket Plugin an unofficial plugin maintained by some of our developers that has shortcodes in it to display a list view:
Event Rocket
I can help answer a couple more questions to get you started, but unable to provide all the coding for a customization.
Let me know.
Thanks