Okay, slight clarification, then.
Your DH is being unreasonable by not helping. Even if he does work, he could help at weekends, he could help for a short period while you implement some kind of sleep training, if that is what you choose.
Your DH is probably not being unreasonable by expressing a preference against co-sleeping. He's entitled to an opinion after all. The biggest problem seems to be that you don't seem able to discuss it, listen to each other and come to an agreement you're both happy with. I know I had a similar problem with XP (exactly the same dilemma actually!) but then he was just incapable of compromise in any form, everything was black or white. I suppose as well that as it's something I feel strongly about I wasn't backing down, but he wasn't listening to my arguments even when I was showing him I'd listened to his, thought about them and come up with answers/solutions or at least reasons why I didn't agree.
I think it can help (if you are able to sit down and discuss this) to try and not focus on each person's preferred method of dealing with it, since they are so dramatically opposed, and instead both state your problems and your end goal and then see if you can come up with some way which meets all of these. It doesn't have to be directly in the middle of the two current options, either, as long as you're both okay with the outcome.
loveglove - You can have sex when they are asleep, especially if you have some kind of setup where you have a bedside cot or extra single bed in the room. Or do it in another room (which tends to be more practical and less creepy when they are older) - I was actually single from when DS was 1 until he was 2, so when I met DP we spent a lot of time on the sofabed! Or at other times. When DS is at the childminder's but I have a day off uni. When his dad used to see him. When used to nap in the pushchair/on the sofa. When he's engrossed in playing trains. We have been known to set him up with some breakfast and CBeebies and go back to bed 
I have a fair few friends who have conceived #2 when still co-sleeping with #1 - I don't know which approach they go for, but they must be managing it somehow. My bigger concern is WTF do you do when they get to be teenagers??