Page layout assignments with XML metadata API

Going by what the Migration Tool produces, these are stored in the profile definitions. Here's an example from one of my org's profiles:

<?xml version="1.0" encoding="UTF-8"?>
<Profile xmlns="http://soap.sforce.com/2006/04/metadata">
  <!-- Field permissions --> 
  <!-- Layout Assignments
   <layoutAssignments>
     <layout>Account-Institution</layout>
     <recordType>Account.Institution</recordType>
   </layoutAssignments>
  <!-- object permssions -->
  <!-- Record Type visibilities -->
  <!-- Tab Visibilities -->
  <!-- User license -->
</Profile>