"I have made it clear that I recognise my part in that and am very willing to change, but although he doesn't want to leave the home and family, he is not actually willing to change his behaviour in return. It probably comes as no surprise that he basically wants his cake and eat it too."
So it sounds to me that you are at the stage where the state of your marriage has been openly discussed between you two, is that correct? If it is, then in my opinion the best chance of your marriage surviving is to NOT let him have his cake and eat it, because if you do, this situation will continue and your self-esteem (and with it your happiness) will be ground into dust; whilst he will feel absolutely entitled to continue having two women dance attendance on him. STOP DANCING. You may feel as if you are throwing away your marriage for pride's sake, but you won't be. Letting this continue is what will make your marriage unretrievable.
You will have to remove the 'have and eat' option from his table. And don't put it to him as a choice - that gives him the power and you begging for crumbs. The position must be stark and uncompromising and he must not be given any choice in the matter. Right now he's treating you as his safety net; he 'might' return if she doesn't work out. Sorry to be so blunt, but it is what it is 
. Let's see how confident he is to fly without that net. He will probably put on a show of confidence to make you weaken, but do not be fooled. If he were confident of a future with her, he'd have left you already .
Tell him it's time for him to arrange somewhere else to stay, that you will no longer be part of this tawdry little triangle. The only choice he has is to move in with her, or move in to his own place. Do NOT accept any objections from him about cost or any other difficulties. Tell him he has made his choice (to start this affair) and he must bear the inevitable consequences of his choice. If he tries to claim the 'have cake and eat it' position, ridicule him. Point out you've already said you will not be part of this triangle, so he has to go. Hold to that position, even when you're crying in front of him. It doesn't weaken your position for him to know that you'd prefer your marriage to survive, but he must be clear that you will not be party to a triangle, ever. Weakening your refusal will simply mean he keeps stringing you both along, bolstering his ego and making him feel all-powerful. (I find people who feel like that start to play with people, be needlessly cruel just to reconfirm they have the power to do so. Don't let yourself be in that position, stay strong for the long run.)
Once he no longer has you as a choice and he's on his own, he will go one of two ways; revel or regret. He may do both, revel and then regret. If he revels in his 'freedom', your marriage was dead already and all that would have happened had you not told him to leave was him stringing you along, using you as a hotel, laundry and restaurant service whilst grinding you into the ground with his disrespect. Instead, by asking him to go you will be in a better position to start your life afresh.
If he regrets - realises he's throwing away what he really wants, then your marriage may survive. May. Infidelity (physical and/or emotional) is a big sledgehammer to take to a marriage. You may decide you no longer trust or respect him, and it's damned hard to love someone without trust and respect. You may jointly decide you've grown too far apart. You may jointly decide to give your marriage another go. I don't know which way it will go. I am only convinced that 'allowing' him this infidelity is a sure-fire marriage-killer.
Give it some thought. Best wishes. ((hugs))