To embed your event on your own website, make sure that it's Public instead of Unlisted. You can do this by editing the event:
Then go into your event and click Share at the top right of the browser:
Copy the Embed code:
And paste it into your website.
Keep in mind the share button is only visible for "Public" and not "Unlisted" events. If you want to grab the embed code for an unlisted event just temporarily make it public to grab the code.
Once embedded into your site the event will show up regardless of whether the Visibility is set to "Public" or "Unlisted". If you ever archive the event in the future, make sure you remove the embed code from your website.
Note that it will embed the entire page, including the chat: