Interval training - proper running?

So I started back running a few months ago and I'm really enjoying it. I get out 2-3 times a week and also mix it up with strength training at the gym. Because I was starting from scratch again I started of running 2 mins / walking 1 min over a mile or 2. I've built it up to running 4 mins & walking 1 min up over 5 miles. Whenever I try to run without stopping I struggle to get past about 2 miles. I find that by taking a minute to get my breath back that I can go further, faster and last longer. My question is: is this proper running? There seems to be a stigma about running where if you stop then it doesn't count. Personally I'm quite happy doing what I do, just wondered what everyone else's thoughts are?

It all counts. If youre struggling to gt past 5 miles then you are probably just running too fast. Slow down and you'll be able to go for longer.

If it's not walking, it has to be running IMHO!!!. Nothing wrong with walk breaks if they help you to do the distance. Cougie is right though, if you slow down a little you might need less of a walk break. At the end of the day you have made a lot of progress, so just keep at it, it's obviously working.