Typically, when a couple buys a home together, both of their names are included as borrowers on the mortgage documents.  Consequently, both parties share the responsibility of making the mortgage payments.  

Even in the event of a separation or divorce, this obligation remains unchanged.  Even if one person moves out, as long as they are listed as a borrower, they are still accountable for meeting the payments, and a failure to do so may result in an adverse credit rating or the bank taking proceedings. 

Of course, other arrangements can be made as well, and lawyers are well placed to assist with negotiating other arrangements.