A little education....
There is a little misunderstanding about what exactly you need here.
Let's talk about midi first.
There reason you are able to hear midi with your current soundcard is because it has a built in tone generator for midi instruments. Midi in itself is just a bunch of Note On and Note Off values, along with some other values such as Volocity (how loud the not should be played) and some other stuff that is of little importance. The point is that you can record all the midi you want, but you need a tone generator to hear it.
These are sometimes called a Wave Synths or whatever. It's job is to take the midi information supplied and create the sound. They usually allow you to define which sound you want to use for the midi part. Blah blah blah.....
You have to have this tone generator to hear midi. Bottom line! There are however programs that will take midi parts and create .wav files of the sound you want.
Now, a soundcards job is usually to provide Analog to Digital (A/D) and Digital to Analog (D/A) conversions for sound coming in and out of the computer. You could wrap that all up by saying it is a A/D/A converter. Without these A/D/A converters, you cannot record sound in the digital realm.
As AlChuck already pointed out, cheaper soundcard provide A/D/A conversion, as well as a Wave Synth right on the card. The downfall is they usually don't do either one all that great. Not that it is the worst sound in the world, but certainly not the kind of quality that is normally associated with big time sound production. The A/D/A converters are usually pretty noisy and don't provide very good conversions, and the Wave Synth's are usually pretty limited in the amount of sound they can create.
Now, AlChuck also pointed out that most upper end soundcards don't have Wave Synth's on them, although, he didn't really clarify that too well. Many good quality soundcards have midi In and Out on them, they just don't have a Wave Synth. This is usually because the more descerning user will have a nice keyboard or a tone generator for midi that will supply the sounds they want. Processing the midi information and creating the sounds also takes a little dsp power, and most of these card I suppose would rather let dedicated units handle these functions.
So, you can find a soundcard that has very nice quality A/D/A converters on it, and will allow midi In and Out on it, but you will need some type of Wave Synth to actually create the sounds from the midi information. There are a few options available to you.
One is that you can usually use two soundcards at the same time in your computer, so you could purchase a nicer soundcard to handle the A/D/A conversions, and use your present card for creating eh midi sounds.
The other is that you can get a keyboard or a tone generator, and purchase a nice soundcard with midi I/O to feed the midi to them them record the keyboard/tone generator sound back into the keyboard with your nice soundcard.
The last is you could live with your crappy card which will do both.
You will not find a nicer soundcard that has a Wave Synth on it that I know of. So in a sense, you are either going to get a nice soundcard where you will need to use another option for midi, or have a crappier soundcard that will handle midi tone generation on it. Many are using the two soundcard approach until they can afford a nice tone generator or keyboard.
The rest of the stuff that has been posted on here is helpful and pertinent to your questions, so I won't elaborate on them anymore as this post is long enough already!
Good luck.
Ed