If you want to implement this (and I pretty much agree with the other posters, this is non-standard and probably shouldn't be done).
You cannot create this ActionBar style with standard APIs (or ActionBarSherlock, for that matter) - since your user interface is non-standard
You can create a RelativeLayout, with your icon in the center (centerInParent = "true"). Then, in the same layout, you can create a background with the width specified as "fill_parent", and a height of up to 2/3 is the size of your center icon (calculate this value in DP).
You can then create ImageButtons for your 2 ActionItems left and right, and then just put them in the layout relative to the center icon.
On the bottom line, you probably should think about your interface in order to make it more standard for design patterns defined by Android. If you still want to do this as your designer asks, you will need to make your own layout (using RelativeLayout, as I suggested, this is one way to achieve the user interface you are looking for).
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