Definitely not both.
The on board card PurpleAngel recommends will get you all the SQ you want for a v. good price.
otoh If you have the cash it makes sense to pair semi pro active monitors with an audio interface. They were designed to compliment one another after all.
An audio Interface would get you at least as good SQ as a PCI on-board - but - it will cost you more money. Which might be difficult to justify when in combination with $300 speakers. So unless you are already planning on upgrading in the future, in which case it would be an investment, it's hard to recommend you spend more than ~$150 on an interface right now. If you had that much money you should spend it on speakers first if you follow me?
There are a couple of good options around at that price.
The NI Audio 2.
http://www.native-instruments.com/en/products/traktor/dj-audio-interfaces/traktor-audio-2/
It was originally designed for DJ use but don't let that put you off as it just happens to fit your needs perfectly for around $100..
The audio quality is pristine as you would expect of a co. wanting to sell professional grade software off the back of the hardware. Why would they risk it?
You can connect your monitors to one set of outputs and your headphones to the other. Each have their own volume control. You don't even have to listen to the same program...
It also works with USB via IPads and smartphones.
Focusrite 2i2
http://uk.focusrite.com/usb-audio-interfaces/scarlett-2i2/specifications
This is slightly more expensive but in addition to the separate outputs and volume controls for speakers and 'phones it has a pair of universal inputs (microphone, line and instrument). The speaker out can be balanced as well which you can take advantage of with your LSR305s. Decent software package too. The 2i4 (extra line outs) and 6i6 (extra ins, outs, S/PDIF and power supply) are good upgrades.
Come to think of it there are many alternative options. Visit a pro audio site and look at the USB audio interface selection. Feel free to ask further questions.