Which filing status to use would depend on a lot things such as total income, the distribution of income between spouses, available tax credits and other things. The best thing to do would be to try it filing joint and then separate to see which gives the better outcome. On average, filing married-joint will give you the better outcome.
Questions you didn't ask may be of some interest to you, since it appears that the newly weds may have low income.
Q. Can you still claim your newly married student as a dependent and get the tuition credit? If so, which way does the family come out better?
For some guidance, see a similar question at
if they elect to file married, jointly, does he need to check yes that someone else could claim him as a dependent?
Yes. If you are claiming him, he still needs to check the box that says someone else can claim him.
as I understand it, I cannot claim him as a dependent, if he files married filing jointly with taxable income, correct?
Only not if they have a tax liability.
If they file to get a refund because tax was withheld (or to get a credit) but they have no tax liability (on Form1040 Line 16) the student MIGHT qualify as your dependent.