H1 resident alien and spouse f1 filing jointly

Technically your wife is not a resident alien but is treated like one for tax filing purposes. With this said, IRS.gov states the following:

Generally, a Nonresident Alien cannot claim an education tax credit unless:

• You are married and choose to file a joint return with a U.S. citizen or resident spouse, or
• You are a Dual-Status Alien and choose to be treated as a U.S. resident for the entire year. 

You might wish to contact the school and quote them this provision in the tax code that permits otherwise non-resident students to receive an educational credit if they file jointly with their resident spouses.

As far as losing her non-resident tax benefits, the only one a can think of is that she will need to report all of her worldwide income rather than exclude any foreign income she might receive. You can file separately from her but if you do, you will lose the educational credit for her. you just need to weigh the pros and cons of filing jointly versus filing separately.