Most banks want some sort of guarantee that you're actually going to pay back your loans. If you're still in school, you don't have any income and won't be able to make payments on said loans. Even with a contract in hand, it's going to be difficult to prove you can pay the amount.
Additionally, residents typically get horrible deals on refinancing because their incomes are so low--you can't get a 5 year repayment plan because you don't have the income to support it, so you end up with variable interest rates, or interest rates very close to your original interest rate with the government.
This is why most people will wait to refinance until after residency. Based on your post, I'm not sure what field your wife is in, but if she's not going to residency, then by all means, refinance as soon as she starts her job.