Invertible jacket?

I am not a native speaker, and I am having trouble finding a correct name for a piece of clothing (such as a jacket or cloak) that can be inverted (turned "inside out") and still be used but would have a different look, color, etc.

"Upside-down jacket"? "Invertible jacket"? Anything else?

The term I'm familiar with is reversible. It's a term used with all types of clothing, even socks!

Here are some examples of reversible jackets:

• Men's Reversible Jackets
• Womens Reversible Coats & Jackets

Reversible or not, cloaks aren't really everyday clothing, so you'll mostly find results for costumes (but that's more about fashion than the English language).