As others have said, it depends how the house was divided in terms of who owns what outright and under what circumstances.
But, assuming the house was split and financially arranged as if you and your parents were 'strangers' each buying their own flat, you could possibly ask the local council if they'd consider a DPA (Deferred Payment Agreement) - I (hopefully) have attached the Age UK information sheet Property and paying for residential care (ageuk.org.uk)
Your DF would have to meet the criteria, the council would have to agree to it and you may incur interest. It's in effect a loan to pay his bills and defer selling the flat until he dies. Obviously you'd have to consider it carefully.
You could then arrange with your siblings to rent out DF's flat. That could go towards his care home bills. That may make the idea more palatable to the council too as they're not footing every penny. The fact that you live downstairs and are a relative with a DH who isn't really well enough to have the stress of moving may help the case for a DPA. I don't know as I've never asked for one but it seems like a reasonable initial thing to discuss with the council.
That way, if it's straight forward and financially worth while, you at least have control over who you have as a tenant and, in theory, you can evict them if they 'break the rules'. You don't have the same power if the flat is sold as it's then highest bidder. The property is making some money towards the care home fees and, possibly, by the time the property has to be sold, it'll be worth a little more. Which may be a good argument for your Dbros.
The biggest obstacle, assuming a DPA is the way forward, is that the property will definitely have to be sold at some point in the future. That day may come quicker than you think sadly. So you do need to decide the way forward. Do you want someone living above you that may be noisier than your parents or do you want to sell the two flats/house? If you've extended your flat it may be worth more so you'd have to divide up into percentages. It becomes complicated so you really do need to speak to both estate agents and solicitors in preparation. You could find that it's a limited market for a house to be converted back into a house and the flat market is buoyant at the time or vice versa.
Make sure you have your ducks in a row whether you sell now or defer. You need to protect yourself and DH. DF is where he is and he's taken care of.