How about you say to your DH its unfair to except your BIL to decide to offer, and you should decide between you two as a couple a range of options you can offer to BIL to pick from, perhaps best sent as an email so that he's got time to read through and decide what he'd like to do.
I'd say options including,
Option 1, would BIL like to buy the house off you and DH, if that's the case, could you 'split the difference' between it's current value and what DH paid (total of what the house cost you and DH, the purchase price, plus interest costs), so that both of them benefit from this arrangement - BIL doesn't have to pay full market rate for a house, your DH benefits from the risk he took for his parents. If this option is taken, then BIL has to have a set time to arrange mortgage etc.
Option 2 would BIL like to just rent the property from you ? If so, you'll give him a discount on the market rent of a similar property, but want a proper tenancy agreement and you will taken on repairs etc as a proper landlord. You can offer another 2/3 months rent free to get used to this shift.
Option 3. Bit of both, agreement to rent for a year then buy it from you.
Option 4. He doesn't want to live there long term, so another 2/3 months rent free until he can line up another property to move to.
All of these options sound fair, you can put a time limit on the rent free times so you aren't saying "pay rent this month" - helps your DH not feel he's taking the piss, allows you to spell out what you are offering to BIL and makes him engage with you.
In the message your DH can say that you don't want to throw him out, and don't want to rip him off, but it's been a year and you need to be able to plan one way or another, if he is planning to leave the property soon (as in the next 6 months), you both need to discuss what to do with it then. (rent or sell), so would like to know.