Most of the new cable boxes include PIP functionality. This is showing up as a common feature and you should check with your local (clueless) cable operator to ask the question of one of their (hopefully) knowledgable customer service representatives.
You will then just plug your cable box into the projector via component video (or HDMI) then press the button that is hiding behind the word PIP.
No, you can't view DVD & a TV channel, but you can see two channels at once. This may NOT be possible on all receivers, but it definitely works on my HD-DVR which I know has two tuners inside of it. Maybe you gotta splurge for the DVR version.
Otherwise, feel free to pick up an outboard PIP generator from Extron for a couple grand.