It depends on whether you are at home or in the hospital.
I decided to have a birth at home with a midwife, and I was lucky enough to find a midwifery group who was still accepting new patients. They told me it would be about $3,200. Which I would have to pay upfront, for my homebirth if my MSP coverage had not kicked in by the 36th week- although that fee also included prenatal care in the 3rd trimester. I think a birth in a hospital would be much more, but they don't give out specific figures.
You might contact The South Community Birthing Clinic, if you are moving to Vancouver. I emailed them several times, and I believe they are very familiar with working with recent immigrants - they also provide some services in many languages, which might be very nice for your wife if English is not her first language, even if she is very comfortable speaking english (especially while she is in labor). I think they are also a charity - so they might be able to deliver the baby for a low cost or free, even if your wife has not yet qualified for MSP. The website is http://scbp.ca/ I decided to just return home in enough time to make sure I will qualify for MSP, because I am the sponsor I could do this easily....
They might be able to answer many of your questions even if you do not intend on living in Vancouver, or could maybe suggest some care providers outside of Vancouver.
Good luck!!