Domestic partnerships are what the kind of legal status that the question is asking about is usually called in Montana. The recognition of these relationships is ad hoc and comes at the local government level or in particular benefit plan arrangements. Montana does not have a state level statute recognizing domestic partnerships, in general and for all purposes.
At least some government agencies in Montana allows employees to designate a domestic partner for employee benefits purposes.
At least some health insurance companies in Montana also allow coverage of domestic partners.
At least one municipal government in Montana, the City of Missoula, has a domestic partnership registry, which can be used to show proof of the existence of a domestic partnership for other purposes.
Montana, like most states, allows people who are not married to enter into enforceable contracts related to economic matters in shared household, often called cohabitation agreements. So long as none of the consideration for the agreement is sex and sex in not required by the agreement or purports to be bindingly consented to in the agreement. (Cohabitation agreements that do so are called meretricious and are void as a matter of public policy because they constitute agreements to engage in illegal conduct, i.e. prostitution.)
People who are not married can also name each other as death beneficiaries of assets, in a will or trust, or as agents in powers of attorney for each other. Some employee benefit plans require that a power of attorney be in place between the parties to recognize them as domestic parters for employee benefit purposes.
Montana does recognize common law marriage, but you are correct that the legal status of a common law marriage once established, is no different than any other kind of marriage and may only be terminated by divorce. Montana does not have the equivalent of a de facto relationship statute like the ones found in Australia and Texas.
Also, Montana, like all U.S. states, is required as a matter of constitutional law to allow same sex couples to legally marry.