I think you're asking the wrong question here, but I'm going to answer it as given, in the hope that this helps clear things up.
If I make my website open source, does it include page content?
Do open source licenses such as GPL or MPL include page content such as text and such within the open source file, or just code, therefore layout?
If you're creating a piece of software to run your website, you can license that software under an open source software license, such as GPL or MPL, or indeed others like AGPL or BSD.
However, if you're just, say, installing WordPress (or some similar product), creating a theme and writing content, then you're not creating a piece of software, so there's nothing to apply a software license to (regardless of open source or not). Similarly, if you're writing a good old-fashioned website in plain HTML and CSS, with nothing dynamic/interactive in it, then again there's no software there to license.
If you wish to release the theme/layout of your website under an open license, software licenses aren't really the right tool for the job (they have been used for this, but it creates some complications). Normally, you'd use a Creative Commons license, or something similar, if you wanted to do that. These (non-software) licenses can also be used for the content, but it's up to you to choose how much of your work to release under a particular license. If you wish to only release the theme/layout, and not the content, you can easily state something like "Theme released under CC-BY-SA, content © All Rights Reserved".
If you're creating a piece of software and a theme and the content, you could state "Powered by SoftwareProductName released under AGPL. Theme released under CC-BY-SA. Content © All Rights Reserved." (Or whatever licenses you wish to use.) Of course, you'd need to read up the specifics on the correct way to use each license you choose.
Because if I go open source for my website can someone just host a duplicate and try to do a phishing operation where I can't do anything to stop them except for DMCA for images, but what about page content such as text?
This was answered in a comment.
Using a software license won't do anything to stop phishing operations. Software licenses are legal tools, not technical ones; they don't prevent anyone doing anything, they just give you the right to bring certain legal actions against someone who goes against your license. Phishers will do what they do, license or no license.
So, go ahead and choose the license(s) you think work best for you, but don't base that choice on what you think phishers and other cybercriminals will do.