You need two queries for this. Let’s say the ID of the featured category is 5. Then you set up two queries retrieving 3 posts each:
$query1 = new WP_Query( array( 'cat' => '5', 'posts_per_page' => 3 ) );
$query2 = new WP_Query( array( 'cat' => '-5', 'posts_per_page' => 3 ) );
Now you have two sets of posts with a maximum of three items. There might be less. I don’t know how you want to handle that situation, but assuming you want an even amount of posts you would loop through them like this:
while ($query1->have_posts() && $query2->have_posts()) {
...
$query1->the_post()
echo '<h1>' . the_title() '</h1>';
echo '<div class="post-content">' . the_content() . '</div>'
...
$query2->the_post()
echo '<h1>' . the_title() '</h1>';
echo '<div class="post-content">' . the_content() . '</div>'
...
}
Note: I didn’t test this code, so beware of typos and so on.