There's a workaround I've found that allows you to open .mht links from the web in a new Chrome tab:
- Install the "IE Tab" Chrome plugin
- Right click on the IE Tab icon in the Chrome tool bar and choose "IE Tab Options" -> "Options"
- Enable (click the checkbox) for the "Enable Auto URLs" option
- To allow .mht files to automatically download when clicked upon in Chrome, add the most specific URL you can come up with to the "Auto URLs" section of the IE Tab settings. For example, "http://your-trusted-intranet-server.your-company.com/*.mht"
- Close the IE Tab options page
If you then want them to automatically open in a Chrome tab, you'll need to do the following steps in addition:
- Download a .mht file to your local disk.
- Right-click on it and choose "Open With".
- Enable (Check the box) for the option that says "Always use this app to open .mht files".
- Choose chrome.exe, or use the "choose another app" option and navigate to "C:\Program Files (x86)\Google\Chrome\Application\chrome.exe" (or wherever Chrome is installed on your PC)
- Go back to the IE Tab options page, and add the most specific local-disk URL you can come up with that matches where the .mht files are downloaded to by IE Tab when you click on them. For example, "file:///C:/Users/your_name/AppData/Local/Microsoft/Windows/INetCache/*.mht"
- Close the IE Tab options page
At this point, when you click on a .mht URL matching the wildcard you've set up in step (5), you should see a tab open in chrome, and a dialog will ask you if you want to open the file. Click "Open" and the file will open in Chrome, using an embedded IE instance running in the Chrome tab.
This only works on Windows PCs (because it allows an IE instance to run inside a Chrome web page), but that's good enough for my requirements.