If you file a joint return with your spouse, then no one can claim you as a dependent, no matter what other tests you meet.
If you file as "married filing separately", then your parent can claim you as a dependent if you meet the usual tests (where you lived, your age, your financial support, and so on.) You would check the box on your MFS return "I can be claimed as a dependent on someone else's return."
As far as filing MFS or MFJ with a non-resident spouse, read below,
If you are a US taxpayer (citizen or resident alien) married to a non-resident alien you have two choices.
You can file as married filing separately. You do not list your spouse as a dependent. Leave the spouse's SSN blank. You can't e-file. Print your return, write "NRA" for the spouse's SSN, and mail in your return. Married filing separately has the highest tax rates and many deductions and credits are reduced or disallowed.
Or, you can make an election to treat your spouse as a US person for tax reasons, in which case you can file as married filing jointly. Treating your spouse as a US person means you must report and pay US income tax on their income from anywhere in the world (there is an offsetting credit for foreign taxes). You get lower tax rates and some other benefits by filing jointly, but the worldwide tax thing might cost you more than you save. Your spouse needs an ITIN (international tax ID number). If you have it, you can e-file the MFJ return. If your spouse does not yet have an ITIN, you can't e-file. You need to print your return and mail it to the IRS, along with a form W-7 ITIN application and any required proofs. You will need a fake SSN to get through the interview, try 999-88-9999. After printing the return, cover the fake SSN with white-out. Mail your return and form W-7 to the address in the W-7 instructions, not the usual address for your tax return.
https://www.irs.gov/uac/about-form-w7
https://www.irs.gov/individuals/international-taxpayers/nonresident-spouse-treated-as-a-resident
