The typical arrangement is known as Tenants-in-Common (TIC), in which you each own a specific share of the property. A 50-50 split is the norm, but if one of you is going to contribute more money, then you can adjust the percentages.
TIC is not always the best choice, though. I recommend consulting an attorney who has solid experience in estate planning—because when you make such a large investment, it's smart to consider the ultimate worst-case scenario: What if one of you were to die during your partnership? This is where a TIC arrangement can get sticky. If your housemate dies, her share of the house will go to whomever she named as heir in her will. So, for instance, you could find yourself suddenly co-owning a home with your former housemate's nephew.
Consider another ownership option: Joint Tenancy with Right of Survivorship. In this setup, you both own the home; if one of you dies, the survivor takes control of the house until she chooses to sell it.