Yeah, the bank doesn't care about the relationship among the people buying the house. Friends can buy property together, family members, business partners, whatever. What matters is how you decide to hold the title. I know in CA married folks tend to hold property in joint tenancy unless they make an effort to change it. I don't know about community property laws in AZ, but you should be able to stipulate how you all want to hold title on the house.
Pan Female, Hinge in a V between my mono (straight) husband, Monochrome and my poly (pan) partner, ThatGuyInBlack