...but because we both need to actually hear what I'm playing wouldn't I come through on the vocal and guitar recording? That's the problem I'm imagining.
So far the best idea I have is to record the video and set up the mic in an even part of the room, then make sure our levels are audibly as they should be (like a live show would be) and record everything through the mic. After the performance is done,
The camera might actually have an XLR input too.
Headphones. (You might need a mixer to create the headphone mix.) Professional studios use headphones, isolation booths, direct-inputs for electric guitars, etc. And/or they often record the instruments & vocals one at time. Or with enough microphones, you can record "live" and you can get enough isolation for a multi-track recording. However, you won't get complete isolation so you won't be able to re-take and replace a track.
You'll have to experiment with microphone location/position. Of course, the acoustics of the room and background noise can present problems too. The way we hear the sound is different from the way a recording sounds, and generally you need to get the mic close to the source to minimize the "room sound". More mics helps too.
If you have an XLR mic, and you don't have an audio interface with an XLR connector, that will give you the best results. All performance/recording mixs are low-impedance balanced with XLR connectors, and they do not interface with a regular soundcard (high-impedance unbalanced). And the mic input on most souncards is worthless for quality recording.
I get best results by recording audio and video simultaneously but separately. I then use audio production software to make the audio sound good then combine it with video with video editing software. You may need a separate monitoring system so that you can hear yourself and each other. This is hardware intensive with a steep learning curve. Or you can plug the MPC1000 into a guitar amp and stick a mic in the middle of the room...