The answer is pretty straightforward, but it still took me a few days to figure it out:
Intent printIntent = new Intent(Intent.ACTION_SEND);
printIntent.setType("text/html");
printIntent.putExtra(Intent.EXTRA_TITLE, "some cool title for your document");
printIntent.putExtra(Intent.EXTRA_STREAM, uri);
startActivity(printIntent);
That's the correct way to do it. Important: Intent.ACTION_SEND_MULTIPLE
does NOT work at the moment.