The rule of thumb is the longer it takes for you to recover from an effort during an interval, the less fit you are. If you have to take a long time after you finish your workout to recover, then it may be time to see a doctor.
Your 15 minute post recovery doesn't seem so bad. But 2 and a half minutes to drop 40 beats seems a bit much.
You'll find over time, though, that you'll be able to drop your heart rate. Or it may be that your recovery time for your interval isn't long enough.
If you're going to do anaerobic intervals, it should be about 1:2 at the least. So if you do a 30 second work effort anaerobic, your recovery time should be a minute. Within that minute, you should be able to drop your heart rate quickly. The quicker you drop that heart rate, the more time your body can recover, so when you start your next interval, your body is ready to go. If you did that 30 second effort (this is just an example), and it took the full minute to get your heart rate down, really... you won't have enough recovery time to do the next effort.
Don't push intervals. They should be progressive, and it should reflect how well you worked with your conditioning phase of your training. If your intervals suck (for lack of a better word), you'll have to go back to the basics.
Good luck.
Koffee