Is a Banana a Herb?

I was told that a banana is not a fruit but a herb. Is this true or are they pulling my leg?

Technically, it's true. But your friends are referring to the botanical definition of a "herb" or "herbaceous plant", i.e., a plant that does not have persistent above ground vegetation like a tree or shrub does. A petunia is a herbaceous tender perennial because the stems never get woody. Rosemary, on the other hand, is not a herb or herbaceous perennial because its stems do become woody and do persist for more than one season.
By the common meaning of the word "herb" a petunia is not a herb, but rosemary is, because rosemary can be used for flavouring food. Banana is not normally considered a herb in this sense because it used mostly as a food, not as seasoning in food.