Unmarried couple and I want to move out of co-owned house

Depending upon the technical way in which you own the house together, you may be able to force a sale, which would be best for you. Talk to a good local lawyer. Good luck.

You probably are obligated on the mortgage note, but also have half ownership of the house.  But the details matter.  When you bought the house, if you signed the mortgage NOTE--which is not the same as the mortgage--you would be liable to the lender, just like he is if he also signed the NOTE.  The other important detail is how you hold title to the property, how your names are shown on your deed.  If it shows his name and yours, you own it together.  It might also add "joint tenants" or "joint tenants with rights of  survivorship".  How you hold title will control your right to compel a sale of the property.  If there is no qualifier or only "joint tenants", you can bring a partition action to force a sale of the property.  That is powerful leverage to persuade him to refinance to a loan in just his name or to sell the property, and pay you for your equity in the property. You need to bring your deed, mortgage, and mortgage note to a real estate attorney who can determine your legal obligations and rights and drive this to resolution.