Purchase as Tenants in Common. This title structure allows each party to then devise their ownership percentage to heirs of their choice – i.e. their own biological children.
Own the property in the %’s of the down payment. I.E. if one person puts down 60% of the DP, and the other 40%, one owns 60% and one 40%. (any percentages will do that reach 100%)
Pay the Mortgage, Interest, Property Tax, Upkeep, etc. in %’s of ownership.
When the house is sold, proceeds and costs also divided in % of ownership.
Consider that upon the death of the other (i.e. the first to go) that the living person will receive a Life Estate for the occupancy of the entire house for their life, and title and ownership will pass to the heirs only upon death of 2nd person. This gives the living person the right to stay in the house without the other’s children forcing a sale or moving into the house. The dead person’s estate would pay for the continuing % of all costs / repairs, etc. Life insurance can fund this.
Agree, in advance, what criteria will be used to determine when the house will be sold, i.e. what if one party cannot pay their %, or decides to terminate the relationship, etc. Will they have a right of first refusal to buy the other out? How will the value be decided (i.e. appraisal). Have these criteria spelled out in advance of the purchase.
State in the agreement what are the responsibilities of each person, i.e. cleaning / gardening / maintenance done by outside company paid in % of ownership, or split division of duties in the agreement . . . i.e. one will pay the bills and manage the garden, other will maintain the exterior of the house and systems, etc. The more you can spell this out PRIOR to arguments, the easier it will be to manage.
Make this easy on yourselves. If the monthly "nut" is $8,000, plus then you have property taxes, insurance and other non-monthly expenses, establish a bank account where the parties contribute, say, $6,000 and $4,000 each (in $ of ownership) monthly, and all agreed upon expenses of the real estate (mortgage, utilities, services, etc) are paid from that joint account. This simplifies the accounting and keeps it all in one place for ease in tracing if it is ever required.