If you are using the twentyeleven theme which it looks like you are, there is a function called twentyeleven_posted_on(), on line 24 within your content.php file. If you want to move the posted on below then move this piece of code ->
<?php if ( 'post' == get_post_type() ) : ?>
<?php twentyeleven_posted_on(); ?>
</div><!-- .entry-meta -->
<?php endif; ?>
Down to the footer section, look at line 55 or do a search on your IDE for "posted in". You'll see some code like the following ->
<?php printf( __( '<span class="%1$s">Posted in</span> %2$s', 'twentyeleven' ), 'entry-utility-prep entry-utility-prep-cat-links', $categories_list ); ?>
Either comment out this code or remove it and replace it with the above code.
Just so you know, when you looked at your page.php file you will notice a function call to ->
<?php get_template_part( 'content', 'page' ); ?>
This is calling the content-page.php file. Even within this you won't find the changes you want to make because it appears your blog page is calling index.php. Within index.php this is calling the following ->
<?php get_template_part( 'content', get_post_format() ); ?>
This will load the content.php file with your posted on and posted in code e.t.c.
Hope this helps