In my area, that includes the following:Race, Color, Religion, Sex, Familial Status, National Origin, Disability, Military Status, Sexual Orientation, Age, Creed, Marital Status, Gender Identity, Source of Income, Immigration and Citizenship StatusBeing 19 y/o, the tenant is feels that this is unfair treatment based on age.

Just be careful on tax treatment and be aware that you will end up with two properties that essentially 100% financed.

If they come in as partners, they can deduct the interest expenses directly against their share of income from partnership.If they come in as lender, they can still deduct the interest as investment interest but might be limited depending on various other factors such as need to itemizing deductions rather than standard deduction. 

Another wrinkle is that I was debating whether it'd be a good idea to get a HELOC on our house as another source of capital, but would that also be factored into my DTI?

It’s never been a factor to me. 

There are a lot of factors to consider, but it's generally worth it.

Opportunity cost is definitely something to factor in as well.

Also, make sure to factor in the implications of future inflation on your assets. 

This is without factoring in the cost of hiring a property manager (I do include mello-roos, solar costs, and ~10% vacancy rate - jeez these are expensive). 

DTI is an important factor when determining how much house you'll be able to afford.