OK, my husband fixed it for me, but I thought I'd share a little bit.
You need this file: tpl_modules_products_all_listing.php, which is in \includes\templates\template_default\templates.
Copy the whole templates folder into includes\templates\classic before you make changes.
The description - look for $display_products_description - is under the picture, because it is in its own row in the table. What you have to do is to remove the row and copy the code into the same column as the name. Make sure you put it inside the "if" statement that checks for the name so you will only have one description per name.

Here's the code:
Code:
if ($disp_sort_order->fields['configuration_key'] == 'PRODUCT_ALL_LIST_NAME')
{
echo $display_products_name;
if (PRODUCT_ALL_LIST_DESCRIPTION > '0')
{
echo $display_products_description;
echo '<br /><br />';
}
}