What is this type of split ownership agreement called?

I was told that sometimes two people will create an agreement where one person will pay for the down payment on a house(normally as an investment, and often doesn't live in the house) while another person pays the monthly payments, and they share ownership of the house.

Does anyone know what this type of agreement is called and where I can find out more information of what normal terms are for it? I know 20% down should get more than 20% of the house, since future dollars are worth less, but not quite sure how much it would be, and not sure how things like property taxes would normally be handled.
A trusted family member is interested in something like this.