I am in a similar situation. Unplanned pregnancies happen even to people that take precautions and are on birth control. No method of birth control is 100% effective! Not even male or female sterilization!
At first I would help your husband assess your financial situation - is it really as dire as you think or is there room for improvement. What are your regular expenses and is there a way to cut them. Which of your expenses are really luxuries and what are the things that you NEED.
A new child will add some expenses, but especially if you are breastfeeding and cloth diapering additional monthly expenses can be kept to a minimum. Our biggest additional monthly expense will be an extra $100 in health insurance, which is outweighed by a few other things falling away this summer anyways.
IMO anyone that has any sort of high interest debt to pay down (car payments, credit card payments) should be paying off their obligations first before even considering buying a bigger house. Saving up money does NOT make sense when you are spending a bunch on interest and finance charges.
Also many people overestimate the size of house they need. Are you REALLY running out of room or are your expectations and your stuff just out of control.
When I was a kid it was perfectly normal and acceptable for siblings to share a room for example, we did not have a bedroom and an extra playroom and we did not have so many toys and clothes that you couldn't fit all of them (for two kids) in one closet.
Nobody needed a "master bedroom suite", the family room was the living room and walk in closets was something that only rich people had in their mansions. THAT was middle class life in the the 70's and 80's and it was fine, everyone was happy.
My husband also feels the financial burden lasting heavily on his shoulders. I have to say while I try to be understanding, part of me wants to yell at him and tell him "tough luck, welcome to being an adult". Yes we are responsible to financially support ourselves and our children, yes we have to work hard. Well, that's life.
How can you help him? I am not sure you can - I am not sure I can. People react differently to unexpected things happening to them. I tend to jump into action, change my plans accordingly and try to accept the new circumstances and make the best of it. Some people (like my DH) want to wallow in their grief, anger and disappointment for a while before they pick themselves up and sometimes grudgingly march on.
Sometimes giving your partner some space to come to terms with this in his own ways is the only thing you can do - and make sure you take care of yourself and surround yourself with other sources of support.
Good luck.