Move.
Yeah, I know, that doesn't sound very sympathetic, but some folks do just live in areas where they haven't got a hope of buying outright, so you either rent forever, while house prices continue to rise, or you do something like this, which I have no experience of, but I'd have several concerns, similar to the "jointly and severally" condition attached to joint mortgages - what happens if one party fails to pay their share? Are you protected in some way?
Or you can go somewhere where you *can* afford to buy. You're not "owed" an affordable house just where you want it, but chances are you *can* afford to buy elsewhere. It may be the simplest option when's all said and done.