Do the HTML tags disappear in the Products Editor?

I'm working with the Marketpress plugin and am placing some products in the store. When I create a product and am writing its description I have used some tags for formating the text, like:

<h3 class="pet">Marine Corps Bulldog Camouflage</h3>
<p>This original My Pillow Pets™ Bulldog mascot, designed by Marines for Marines, has digital cammie plush fabric with the Eagle, Globe and Anchor embroidered on its back and a USMC patch on its paw. It also has all the softness and cuddliness of a real puppy! You'll never want to put it down!</p>

OK. When I save the page and go to the browser, clicking in the category related to that product what I have is as following:
Marine Corps Bulldog Camouflage This original My Pillow Pets™ Bulldog mascot, designed by Marines for Marines, has digital cammie plush fabric with the Eagle, Globe and Anchor embroidered on its back and a USMC patch on its paw. It also has all the softness and cuddliness of a real puppy! You'll never want to put...
Both <h3></h3> and <p></p> disappeared.
How to keep all the tags I'm using inside the Product Editor?