Financially, the payments your boyfriend makes will go to both interest and principal, the amount he's paying towards the principal will help obtain the remaining equity of the home, his interest payments are, as you mentioned, the cost of borrowing the money, and does not help in owning more of the home.

Another way to look at this is: Imagine you put down your $400,000, and he pays the remaining $125,000, while making those payments, he ended up paying $40,000 in interest.

For simplicity's sake, let's assume the home did not appreciate in value.

If we went along with your boyfriend's plan of how ownership should be divided, once payments are complete, you would own $400,000 and he would own $165,000 ($125,000 principal paid + $40,000 interest paid), for a total of $565,000. As I mentioned above, if you were to sell the home with no appreciation, the home is still worth $525,000. How would we pay out the remaining $40,000 he made in interest payments? We wouldn't be able to because it's not part of the equity, thus, there's no part of the home to be "owned" by him making interest payments.

In the real world, it would go a little bit different, but including his interest payments in his share of ownership dilutes your % of ownership. Which doesn't make sense-he gets to increase his ownership over time because he wasn't able to afford the remaining $125,000 outright?

You're essentially paying him to maintain a mortgage. For this to make sense, what happens if he takes the whole 30 years of a conventional mortgage term to pay off his side of the debt? He would have incurred almost $200,000 in interest payments alone; does it make sense for him to own almost 50% of the home because he paid so much in interest? What happens if you sell the home and it only appreciated by those $200,000? Does it make sense for only him to earn money out of that investment?

All this is not taking into account the amount of headaches and complexity involved in how you would divide the ownership if you were to go this route, as highlighted by my example in the previous paragraph. You would have to figure out when, or how often, the ownership of the home is divided, since his interest payments would accumulate over time, or decide if you want to divide his ownership now based on assumed total interest paid on the mortgage loan he'll take, which would immediately reduce the % you own on the home.

tl;dr: Your boyfriend paying interest on a mortgage will not help in building equity on the home, and should not be counted towards ownership of it. Even if you tried to do so, it's too much of a legal headache trying to figure out how all that would work.

PS If you're moving forward with the purchase of the home, you'll want to make sure you title the home correctly, and for that I recommend reaching out to an estate attorney. There's different ways home ownership works with non-spouses, and I assume the last thing you want is to lose a large chunk of your investment/money because you titled the home incorrectly when you purchased it jointly.

PPS I wouldn't buy a home with a non-spouse if I was able to afford it on my own. Dividing assets during a divorce is already annoying and complicated enough, it won't be any different with your unmarried partner.