What's Up With This Design Flaw?! HELP!

So I got my new 360 yesterday hoping to use HDMI (for my computer monitor) and componant for my audio (to a different source) but when I plug in the componant cables, it blocks the HDMI port! My guess is that it won't let me use both at the same time anyway but it's pretty frustrating since I currently have no audio. So, what I did was buy an HDMI splitter and an HDMI to componant cable. My plan is to plug in the splitter to the 360, then one HDMI cable to the monitor then the other to my separate audio source both plugged into the splitter. I've got a couple of questions.

1. Will this even work using the two HDMIs?

2. Any other suggestions at all?

Please help me out, it's really annoying and I don't know what to do.

Don't worry your problem is very easy to fix all you have to do is buy this HDMI Cable from Microsoft and it will fix all of your problems. I use it and have had no problems Here's a link to the HDMI cablehttp://www.xbox.com/en-US/hardware/x/xbox360hdmiavcable/