I've been usually saying 'half an hour' but tonight I found 'a half hour' in my book and wonder
it is commonly used expression.
Are both 'half an hour' and 'an half hour' interchangeable?
For me "a half hour" is more AmE. I only really base this on the fact that my friend in Madrid, who was from Portland, Oregon was the first person I heard use it. After that, I started to notice it much more often from other Americans I came into contact with. In BrE, we almost exclusively use "half an hour".