Drifting off topic here, but what's the difference between a data connection
to an XML file which is a resource in a template, and creating your own
instance of the XML DOM loaded from a resource in the template? Other than
the caching being done in a different place? (The data interop example
caches the DOM, though I didn't look closely to see at what time.)

Solution for my problem:

// First create a "COM" DOM and load the xslt resource file into that DOM
IXMLDOMDocument domDocument = thisXDocument.CreateDOM();
domDocument.load("transform.xslt");

// Create an XmlDocument and load the xml of the DOM.
XmlDocument xsltDocument = new XmlDocument();
xsltDocument.LoadXml(domDocument.xml);

// Then load the xml of that DOM into a .Net XmlDocument
XmlDocument xsltDocument = new XmlDocument();
xsltDocument.LoadXml(domDocument.xml);

// Load the InfoPath xml into a .Net XmlDocument
XmlDocument infoPathDocument = new XmlDocument();
infoPathDocument.LoadXml(thisXDocument.DOM.xml);

// Load the xslt into the XslTransform-class
XslTransform xslt = new XslTransform();
xslt.Load(xsltDocument.CreateNavigator(), new XmlUrlResolver(),
this.GetType().Assembly.Evidence);

// And finally perform the transformation and write the output to file:
using (FileStream fs = new FileStream(@"C:\temp\output.xml",
FileMode.Create)) {
 xslt.Transform(infoPathDocument.CreateNavigator(), null, fs, new
XmlUrlResolver());
}

But I still wonder why (in my case) InfoPath can't handle the xslt-file as a
secondary datasource and throws strange exceptions...
Just for the record: I didn't change anything else in my form or in the
xslt-file.