My doctor visits are about $125. Vaccines, depending on how many, run anywhere from $25 to $100 per visit. The worst visit I had was when my son was sick and they had to run a bunch of tests. On top of the doctor visit fee, there was about $500 worth of labs run. With the insurance rates, that went down to about $75. Crazy!
I have an HSA, so all the bills run through the insurance company first, get the insurance rate, and are then paid automatically from the HSA. Try having them bill the insurance first before you pay it to see if you get the cheaper rate. And ask your doctor about payment plan options they may have.
ETA: You'd be saving $1,932 in monthly premiums. That is almost your family deductible. How often do you have $2,400 in medical expenses each year? Does your employer have a medical reimbursement option where they take out money pre tax from his check that can be used for medical expenses? For me, I'd definitely switch to the deductible plan. I pay $110 a month for a $5000 deductible plan and my employer puts $2000 each year into my HSA that rolls over to the next year up to $20,000. So it's really like my deductible is $3000. I also have the option of the pre tax account, but you have to use it all each year, otherwise it is forfeited.
3BoysUnder3: There are a ton of insurance plans. The ones that don't have a copay for doctor visits are usually MUCH cheaper. But the tradeoff is that you pay the deductible first, so you have higher out of pocket expenses. It's not wonky, it's just one of the options available.