Boolean filter with checkbox on AngularJS

I have an array of objects with property published which can be true or false. I'm building a filter to be able to display only published or only not published items.

So far the published one works fine like this:

<input 
   type="checkbox" 
   ng-model="search.published" 
   ng-change="search.published = search.published ? true : undefined"> 
Published

And in the ng-repeat it looks like this:

ng-repeat="exhibitor in filterItems = (data | filter: search)"

The problem comes when I try to add another checkbox to display only unpublished items.

I've tried this with a second checkbox:

<input 
   type="checkbox" 
   ng-model="search.published" 
   ng-change="search.published = search.published ? false : undefined"> 
Unpublished

But of course it can't have the same model as the published items one. Also, the checkbox won't get ticked even if I remove the first checkbox.

Any tips on how to work around this?