You should be able to move the header to above the bar.
Try editing the Theme Header file (header.php).
Near the bottom you will see something like:
<?php $header_image = get_header_image();
if ( ! empty( $header_image ) ) { ?>
<a class="header-image" href="<?php echo esc_url( home_url( '/' ) ); ?>" title="<?php echo esc_attr( get_bloginfo( 'name', 'display' ) ); ?>" rel="home">
<img src="<?php header_image(); ?>" width="<?php echo get_custom_header()->width; ?>" height="<?php echo get_custom_header()->height; ?>" alt="" />
</a>
<?php } // if ( ! empty( $header_image ) ) ?>
This is what generates the header.
Move it to where you want it (above the menu).
Make sure you include all the PHP code in that block so errors don’t happen.
The menu code is above header image and looks like:
<nav id="site-navigation" class="main-navigation" role="navigation">
<button class="menu-toggle"><span class="icon-font icon-menu"></span></button>
<?php wp_nav_menu( array( 'theme_location' => 'primary' ) ); ?>
</nav><!-- #site-navigation -->
In the end, it will look something like:
<?php $header_image = get_header_image();
if ( ! empty( $header_image ) ) { ?>
<a class="header-image" href="<?php echo esc_url( home_url( '/' ) ); ?>" title="<?php echo esc_attr( get_bloginfo( 'name', 'display' ) ); ?>" rel="home">
<img src="<?php header_image(); ?>" width="<?php echo get_custom_header()->width; ?>" height="<?php echo get_custom_header()->height; ?>" alt="" />
</a>
<?php } // if ( ! empty( $header_image ) ) ?>
<nav id="site-navigation" class="main-navigation" role="navigation">
<button class="menu-toggle"><span class="icon-font icon-menu"></span></button>
<?php wp_nav_menu( array( 'theme_location' => 'primary' ) ); ?>
</nav><!-- #site-navigation -->
Note: You may want to move the social links bar as well. You can move it around the same way.