Everyone is spot on! Take some time to applaud each other for the effort you are making...its a really big deal that you both are consciously working at building better communication with each other. Just as you've noticed that you have a tendancy to interrupt him and the negative affect it has, remember that you both are changing the ways that you usually communicate. There are bound to be slip ups, and there will be some escalation. But, as Black Iris, Lyz, and Tbone are suggesting, keep working at it, put in spending time together where you aren't fighting ( couple date nights here and there, pretending to be teens again and making out in the back of the car, stuff to remind you both how good life is with each other), see a counselor if things are getting a little out of hand or if you just can't seem to resolve an issue without getting into a major spat, and try to remember to look at what the core issue is rather than all the other stuff. It helps to stay focused on the real issue.

I'll be honest, I hated having to confront all this stuff the first time a girlfriend wouldn't let me get away with the silent shrug. At times it took me getting really heated up to finally let out what was bothering me...AND THEN SHE WAS HAPPY!?!?! She understood good communication way better than I did, and she knew that I was going to be going through some pretty rough emotions when I finally got to the core of what I was dealing with, so she was patient. VERY patient.

Keep up the awesome work! Really, you both should treat yourselves out to a great evening and maybe even rent a room to make it feel even more special (or to at least not have to worry about waking up the neighbors)!

BookMama is right. If you haven't been communicating then, yeah you are going to unearth some problems and it is going to be frustrating. But if you are both on the same page that is VERY encouraging and you should be encouraged. Try to remember you are on the same team and you are both working toward a common goal.

Couseling sounds like a good idea, especially because if you are having some problems already, it might be easier to get a third parties view on the situation. Contact a church or local medical non-profit for some affordable counseling options.

If you haven't been communicating for a while, you may have to work through a few issues you disagree on. So the fighting might go up for a while.

In addition, it would probably help to spend time together hanging out and building closeness. Having sex also makes people nicer to each other.

However, if you are fighting horribly over small things, you may want to look at the way you are fighting. There are so many thing that could be causing you problems, but here are some I sometimes have to work on -

You need a way to back down and move towards agreement when you are fighting. If not, you can go on forever about some really stupid issue.
You need to be able to look at how your feelings are driving the argument - maybe you're not really upset about the way he did the dishes, you're upset that he watched sports when he could have spent time with you, for example.
You must not, must not bring in everything and the kitchen sink that your partner does wrong when you are discussing something.
Take a break if you need to, just agree when you'll get back to finish.
Don't insult.
Avoid escalation.

And, I agree with Tbone - if you can't work out your arguments, consider getting counseling.

Maybe you need professional counseling. It's admirable that the two of you are trying very hard to talk things out, but sometimes, that objective third party can see something that neither of you can.